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Search: a161835 -id:a161835
Displaying 1-10 of 23 results found. page 1 2 3
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A161839 a(n) = A161835(n)/5. +20
0
5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..55.
CROSSREFS
Cf. A018253, A161344, A161345, A161424, A161425, A161835, A161901.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jun 30 2009
STATUS
approved
A033676 Largest divisor of n <= sqrt(n). +10
137
1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 4, 3, 2, 1, 4, 5, 2, 3, 4, 1, 5, 1, 4, 3, 2, 5, 6, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 6, 7, 5, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 8, 1, 2, 5, 4, 7, 6, 1, 8, 9, 2, 1, 7, 5, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
a(n) = sqrt(n) is a new record if and only if n is a square. - Zak Seidov, Jul 17 2009
a(n) = A060775(n) unless n is a square, when a(n) = A033677(n) = sqrt(n) is strictly larger than A060775(n). It would be nice to have an efficient algorithm to calculate these terms when n has a large number of divisors, as for example in A060776, A060777 and related problems such as A182987. - M. F. Hasler, Sep 20 2011
a(n) = 1 when n = 1 or n is prime. - Alonso del Arte, Nov 25 2012
a(n) is the smallest central divisor of n. Column 1 of A207375. - Omar E. Pol, Feb 26 2019
a(n^4+n^2+1) = n^2-n+1: suppose that n^2-n+k divides n^4+n^2+1 = (n^2-n+k)*(n^2+n-k+2) - (k-1)*(2*n+1-k) for 2 <= k <= 2*n, then (k-1)*(2*n+1-k) >= n^2-n+k, or n^2 - (2*k-1)*n + (k^2-k+1) = (n-k+1/2)^2 + 3/4 < 0, which is impossible. Hence the next smallest divisor of n^4+n^2+1 than n^2-n+1 is at least n^2-n+(2*n+1) = n^2+n+1 > sqrt(n^4+n^2+1). - Jianing Song, Oct 23 2022
REFERENCES
G. Tenenbaum, pp. 268 ff, in: R. L. Graham et al., eds., Mathematics of Paul Erdős I.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = n / A033677(n).
a(n) = A161906(n,A038548(n)). - Reinhard Zumkeller, Mar 08 2013
a(n) = A162348(2n-1). - Daniel Forgues, Sep 29 2014
MAPLE
A033676 := proc(n) local a, d; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := max(a, d) ; end if; end do: a; end proc: # R. J. Mathar, Aug 09 2009
MATHEMATICA
largestDivisorLEQR[n_Integer] := Module[{dvs = Divisors[n]}, dvs[[Ceiling[Length@dvs/2]]]]; largestDivisorLEQR /@ Range[100] (* Borislav Stanimirov, Mar 28 2010 *)
Table[Last[Select[Divisors[n], #<=Sqrt[n]&]], {n, 100}] (* Harvey P. Dale, Mar 17 2017 *)
PROG
(PARI) A033676(n) = {local(d); if(n<2, 1, d=divisors(n); d[(length(d)+1)\2])} \\ Michael B. Porter, Jan 30 2010
(Haskell)
a033676 n = last $ takeWhile (<= a000196 n) $ a027750_row n
-- Reinhard Zumkeller, Jun 04 2012
(Python)
from sympy import divisors
def A033676(n):
d = divisors(n)
return d[(len(d)-1)//2] # Chai Wah Wu, Apr 05 2021
CROSSREFS
Cf. A033677 (n/a(n)), A000196 (sqrt), A027750 (list of divisors), A056737 (n/a(n) - a(n)), A219695 (half of this for odd numbers), A207375 (list the central divisor(s)).
The strictly inferior case is A060775. Cf. also A140271.
Indices of given values: A008578 (1 and the prime numbers: a(n) = 1), A161344 (a(n) = 2), A161345 (a(n) = 3), A161424 (4), A161835 (5), A162526 (6), A162527 (7), A162528 (8), A162529 (9), A162530 (10), A162531 (11), A162532 (12), A282668 (indices of primes).
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane
STATUS
approved
A161344 Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k). +10
53
4, 6, 8, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Define a sieve operation with parameter s that eliminates integers of the form s^2 + s*i (i >= 0) from the set A000027 of natural numbers. The sequence lists those natural numbers that are eliminated by the sieve s=2 and cannot be eliminated by any sieve s >= 3. - R. J. Mathar, Jun 24 2009
After a(3)=8 all terms are 2*prime; for n > 3, a(n) = 2*prime(n-1) = 2*A000040(n-1). - Zak Seidov, Jul 18 2009
From Omar E. Pol, Jul 18 2009: (Start)
A classification of the natural numbers A000027.
=============================================================
Numbers k whose largest divisor <= sqrt(k) equals j
=============================================================
j Sequence Comment
=============================================================
1 ..... A008578 1 together with the prime numbers
2 ..... A161344 This sequence
3 ..... A161345
4 ..... A161424
5 ..... A161835
6 ..... A162526
7 ..... A162527
8 ..... A162528
9 ..... A162529
10 .... A162530
11 .... A162531
12 .... A162532
... And so on. (End)
The numbers k whose largest divisor <= sqrt(k) is j are exactly those numbers j*m where m is either a prime >= k or one of the numbers in row j of A163925. - Franklin T. Adams-Watters, Aug 06 2009
See also A163280, the main entry for this sequence. - Omar E. Pol, Oct 24 2009
Also A100484 UNION 8. - Omar E. Pol, Nov 29 2012 (after Seidov and Hasler)
LINKS
Table of n, a(n) for n=1..56.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
Omar E. Pol, Illustration: Divisors and pi(x)
Omar E. Pol, Illustration of initial terms
Omar E. Pol. Illustration of initial terms of A008578, A161344, A161345, A161424
FORMULA
Equals 2*A000040 union {8}. - M. F. Hasler, Nov 27 2012
a(n) = 2*A046022(n+1) = 2*A175787(n). - Omar E. Pol, Nov 27 2012
MAPLE
isA := proc(n, s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161344 := proc(n) for s from 3 to n do if isA(n, s) then RETURN(false); fi; od: isA(n, 2) ; end: for n from 1 to 3000 do if isA161344(n) then printf("%d, ", n) ; fi; od; # R. J. Mathar, Jun 24 2009
MATHEMATICA
a[n_] := If[n <= 3, 2n+2, 2*Prime[n-1]]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Nov 26 2012, after Zak Seidov *)
PROG
(PARI) a(n)=if(n>3, prime(n-1), n+1)*2 \\ M. F. Hasler, Nov 27 2012
CROSSREFS
Cf. A000005, A018253, A160811, A160812, A161205, A161346, A033676, A008578, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532, A163925.
Second column of array in A163280. Also, second row of array in A163990.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jun 20 2009
EXTENSIONS
More terms from R. J. Mathar, Jun 24 2009
Definition added by R. J. Mathar, Jun 28 2009
STATUS
approved
A161345 Numbers k whose largest divisor <= sqrt(k) is 3. +10
39
9, 12, 15, 18, 21, 27, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381, 393, 411, 417, 447, 453, 471, 489, 501, 519, 537, 543, 573, 579, 591, 597, 633, 669, 681, 687, 699, 717, 723 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Define a sieve operation with parameter s that eliminates integers of the form s^2+s*i (i >= 0) from the set A000027 of natural numbers. The sequence lists those natural numbers that are eliminated by the sieve s=3 and cannot be eliminated by any sieve s >= 4. - R. J. Mathar, Jun 24 2009
See A161344 for more information. - Omar E. Pol, Jul 05 2009
See also the array in A163280, the main entry for this sequence. - Omar E. Pol, Oct 24 2009
Union of {12, 18, 27} and all the numbers of the form 3*p, where p is an odd prime. - Amiram Eldar, Apr 17 2024
LINKS
Table of n, a(n) for n=1..55.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Omar E. Pol, Illustration: Divisors and pi(x).
Omar E. Pol, Illustration for A008578, A161344, A161345 and A161424. [From Omar E. Pol, Oct 24 2009]
FORMULA
Numbers k such that A033676(k)=3. - Omar E. Pol, Jul 05 2009
MAPLE
isA := proc(n, s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161345 := proc(n) for s from 4 to n do if isA(n, s) then RETURN(false); fi; od: isA(n, 3) ; end: for n from 1 to 3000 do if isA161345(n) then printf("%d, ", n) ; fi; od; # R. J. Mathar, Jun 24 2009
MATHEMATICA
md3Q[n_]:=Max[Select[Divisors[n], #<=Sqrt[n]&]]==3; Select[Range[800], md3Q] (* Harvey P. Dale, Aug 12 2013 *)
CROSSREFS
Cf. A000005, A018253, A160811, A160812, A161205, A161344, A161346, A033676, A008578, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
Third column of the array in A163280. Also, third row of array in A163990. - Omar E. Pol, Oct 24 2009
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jun 20 2009
EXTENSIONS
Terms beyond a(10) from R. J. Mathar, Jun 24 2009
Definition added by R. J. Mathar, Jun 28 2009
STATUS
approved
A163280 Square array read by antidiagonals where column k lists the numbers j whose largest divisor <= sqrt(j) is k. +10
30
1, 2, 4, 3, 6, 9, 5, 8, 12, 16, 7, 10, 15, 20, 25, 11, 14, 18, 24, 30, 36, 13, 22, 21, 28, 35, 42, 49, 17, 26, 27, 32, 40, 48, 56, 64, 19, 34, 33, 44, 45, 54, 63, 72, 81, 23, 38, 39, 52, 50, 60, 70, 80, 90, 100, 29, 46, 51, 68, 55, 66, 77, 88, 99, 110, 121, 31, 58, 57, 76, 65, 78, 84, 96, 108, 120, 132, 144 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence is a permutation of the natural numbers A000027. Note that the first column is formed by 1 together with the prime numbers.
Column k contains exactly those numbers j=k*m where m is either a prime >= j or one of the numbers in row k of A163925. - Franklin T. Adams-Watters, Aug 12 2009
LINKS
Table of n, a(n) for n=1..78.
Omar E. Pol, Illustration of initial terms of column 1: A008578
Omar E. Pol, Illustration of initial terms of column 2: A161344
Omar E. Pol, Illustration of initial terms of columns 1-4: A008578, A161344, A161345, A161424
Index entries for sequences that are permutations of the natural numbers
FORMULA
Column k lists the numbers j such that A033676(j)=k.
EXAMPLE
Array begins:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, ...
3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, ...
5, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, ...
7, 14, 21, 32, 45, 60, 77, 96, 117, 140, 165, 192, ...
11, 22, 27, 44, 50, 66, 84, 104, 126, 150, 176, 204, ...
13, 26, 33, 52, 55, 78, 91, 112, 135, 160, 187, 216, ...
17, 34, 39, 68, 65, 102, 98, 128, 153, 170, 198, 228, ...
19, 38, 51, 76, 75, 114, 105, 136, 162, 190, 209, 264, ...
23, 46, 57, 92, 85, 138, 119, 152, 171, 200, 220, 276, ...
29, 58, 69, 116, 95, 174, 133, 184, 189, 230, 231, 348, ...
31, 62, 87, 124, 115, 186, 147, 232, 207, 250, 242, 372, ...
...
MAPLE
A163280 := proc(n, k) local r, T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then RETURN(T) ; fi; fi; od: end: # R. J. Mathar, Aug 09 2009
MATHEMATICA
nmax = 12;
pm = Prime[nmax];
sDiv[n_] := Select[Divisors[n], #^2 <= n&][[-1]];
Clear[col]; col[k_] := col[k] = Select[Range[k pm], sDiv[#] == k&];
T[n_, k_ /; 1 <= k <= Length[col[k]]] := col[k][[n]];
Table[T[n-k+1, k], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 15 2019 *)
CROSSREFS
Rows 1-12: A000290, A002378, A005563, A164004, A100451, A164006, A164007, A164008, A164009, A164010, A164011, A164012.
Columns 1-12: A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
Another version: A163990.
Cf. A000027, A000040, A033676, A147861, A163100, A164000.
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Aug 07 2009
EXTENSIONS
Edited by R. J. Mathar, Aug 01 2010
Example edited by Jean-François Alcover, Dec 15 2019
STATUS
approved
A161424 Numbers k whose largest divisor <= sqrt(k) equals 4. +10
28
16, 20, 24, 28, 32, 44, 52, 68, 76, 92, 116, 124, 148, 164, 172, 188, 212, 236, 244, 268, 284, 292, 316, 332, 356, 388, 404, 412, 428, 436, 452, 508, 524, 548, 556, 596, 604, 628, 652, 668, 692, 716, 724, 764, 772, 788, 796, 844, 892, 908, 916, 932, 956, 964 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Define a sieve operation with parameter s that eliminates integers of the form s^2 + s*i (i >= 0) from the set A000027 of natural numbers. The sequence lists those natural numbers that are eliminated by the sieve s=4 and cannot be eliminated by any sieve s >= 5. - R. J. Mathar, Jun 24 2009
See A161344 for more information. - Omar E. Pol, Jul 05 2009
See also the array in A163280, the main entry for this sequence. - Omar E. Pol, Oct 24 2009
LINKS
Table of n, a(n) for n=1..54.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
Omar E. Pol, Illustration: Divisors and pi(x)
Omar E. Pol, Illustration for A008578, A161344, A161345 and A161424 [From Omar E. Pol, Oct 24 2009]
FORMULA
Numbers n such that A033676(n)=4. - Omar E. Pol, Jul 05 2009
MAPLE
isA := proc(n, s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161424 := proc(n) for s from 5 to n do if isA(n, s) then RETURN(false); fi; od: isA(n, 4) ; end: for n from 1 to 3000 do if isA161424(n) then printf("%d, ", n) ; fi; od; # R. J. Mathar, Jun 24 2009
MATHEMATICA
Select[Range[1, 1000], Function[m, Max[Select[Divisors[m], # <= Sqrt[m] &]] == 4]] (* Ashton Baker, Nov 03 2013 *)
CROSSREFS
Cf. A000005, A018253, A160811, A160812, A161205, A161344, A161345, A161346, A161425, A161428, A033676, A008578, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532.
Cf. Fourth column of array in A163280. Also, fourth row of array in A163990. - Omar E. Pol, Oct 24 2009
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jun 20 2009
EXTENSIONS
Terms beyond a(8) from R. J. Mathar, Jun 24 2009
Definition added by R. J. Mathar, Jun 28 2009
STATUS
approved
A162527 Numbers k whose largest divisor <= sqrt(k) equals 7. +10
19
49, 56, 63, 70, 77, 84, 91, 98, 105, 119, 133, 147, 161, 175, 203, 217, 245, 259, 287, 301, 329, 343, 371, 413, 427, 469, 497, 511, 553, 581, 623, 679, 707, 721, 749, 763, 791, 889, 917, 959, 973, 1043, 1057, 1099, 1141, 1169, 1211, 1253, 1267, 1337, 1351 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A161344 for more information.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..10000
FORMULA
Numbers k such that A033676(k)=7.
MAPLE
A033676 := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n), list)) ; op(floor((nops(dvs)+1)/2) , dvs) ; end: for n from 1 to 2000 do if A033676(n) = 7 then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jul 13 2009
MATHEMATICA
ld = 7;
selQ[n_] := AllTrue[Divisors[n], # <= ld || #^2 > n&];
Select[Range[ld, 200] ld, selQ] (* Jean-François Alcover, Apr 14 2020 *)
ld7Q[n_]:=Select[Divisors[n], #<=Sqrt[n]&][[-1]]==7; Select[Range[1400], ld7Q] (* Harvey P. Dale, Jan 13 2023 *)
CROSSREFS
Cf. A033676, A008578, A161344, A161345, A161424, A161835, A162526, A162528, A162529, A162530, A162531, A162532.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 05 2009
EXTENSIONS
More terms from R. J. Mathar, Jul 13 2009
STATUS
approved
A162528 Numbers k whose largest divisor <= sqrt(k) equals 8. +10
19
64, 72, 80, 88, 96, 104, 112, 128, 136, 152, 184, 232, 248, 296, 328, 344, 376, 424, 472, 488, 536, 568, 584, 632, 664, 712, 776, 808, 824, 856, 872, 904, 1016, 1048, 1096, 1112, 1192, 1208, 1256, 1304, 1336, 1384, 1432, 1448, 1528, 1544, 1576, 1592, 1688 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A161344 for more information.
LINKS
Table of n, a(n) for n=1..49.
FORMULA
Numbers k such that A033676(k)=8.
MAPLE
A033676 := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n), list)) ; op(floor((nops(dvs)+1)/2) , dvs) ; end: for n from 1 to 2000 do if A033676(n) = 8 then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jul 13 2009
MATHEMATICA
ld8Q[n_]:=Last[Select[Divisors[n], #<=Sqrt[n]&]]==8; Select[Range[ 2000], ld8Q] (* Harvey P. Dale, Apr 08 2017 *)
CROSSREFS
Cf. A033676, A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162529, A162530, A162531, A162532.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 05 2009
EXTENSIONS
More terms from R. J. Mathar, Jul 13 2009
STATUS
approved
A162530 Numbers k whose largest divisor <= sqrt(k) equals 10. +10
19
100, 110, 120, 130, 140, 150, 160, 170, 190, 200, 230, 250, 290, 310, 370, 410, 430, 470, 530, 590, 610, 670, 710, 730, 790, 830, 890, 970, 1010, 1030, 1070, 1090, 1130, 1270, 1310, 1370, 1390, 1490, 1510, 1570, 1630, 1670, 1730, 1790, 1810, 1910, 1930 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A161344 for more information.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
Numbers k such that A033676(k) = 10.
MAPLE
filter:= n -> andmap(t -> t<=10 or t^2 > n, numtheory:-divisors(n)):
select(filter, [seq(n, n=100..10000, 10)]); # Robert Israel, Aug 16 2018
MATHEMATICA
ld10Q[n_]:=Last[Select[Divisors[n], #<=Sqrt[n]&]]==10; Select[Range[2000], ld10Q] (* Harvey P. Dale, Jan 30 2011 *)
CROSSREFS
Cf. A033676, A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162531, A162532.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 05 2009
EXTENSIONS
More terms from Gerard P. Michon, Jul 12 2009
STATUS
approved
A162532 Numbers k whose largest divisor <= sqrt(k) equals 12. +10
19
144, 156, 168, 180, 192, 204, 216, 228, 264, 276, 348, 372, 444, 492, 516, 564, 636, 708, 732, 804, 852, 876, 948, 996, 1068, 1164, 1212, 1236, 1284, 1308, 1356, 1524, 1572, 1644, 1668, 1788, 1812, 1884, 1956, 2004, 2076, 2148, 2172, 2292, 2316, 2364 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A161344 for more information.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
Numbers k such that A033676(k)=12.
MAPLE
A033676 := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n), list)) ; op(floor((nops(dvs)+1)/2) , dvs) ; end: for n from 1 to 3500 do if A033676(n) = 12 then printf("%d, ", n) ; fi; od: # R. J. Mathar, Jul 13 2009
MATHEMATICA
ld12Q[n_]:=First[Select[Reverse[Divisors[n]], #<=Sqrt[n]&]]==12; Select[ 12*Range[ 200], ld12Q] (* Harvey P. Dale, Mar 29 2013 *)
CROSSREFS
Cf. A033676, A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 05 2009
EXTENSIONS
More terms from R. J. Mathar, Jul 13 2009
STATUS
approved
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