Revision History for A173581
(Underlined text is an addition;
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#10 by Wesley Ivan Hurt at Thu Nov 09 20:37:56 EST 2023
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#9 by Wesley Ivan Hurt at Thu Nov 09 20:36:44 EST 2023
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| NAME
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Numbers nk such that tau(sigma(nk)) = rad(n)k).
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| COMMENTS
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rad(n) is the product of the primes dividing n (A007947 ) ), tau(n) is the number of divisors of n (A000005) ), and sigma(n) is the sum of divisor of n (A000203).
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| FORMULA
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nNumbers k such that A062068(n)= k) = A007947(n)k).
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| EXAMPLE
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2 is a member, since sigma(2) = 3, tau(3) = 2 and rad(2) = 2 sigma(65856) = 203200, tau(203200) = 42 and rad(65856) = 42.
65856 is a member, since sigma(65856) = 203200, tau(203200) = 42 and rad(65856) = 42.
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| CROSSREFS
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Cf. A000005 (tau), A000203 (sigma) A007947 (rad), A062068.
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| STATUS
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approved
editing
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#8 by Charles R Greathouse IV at Mon Apr 03 10:36:12 EDT 2023
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| LINKS
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C. K. Caldwell, <a href="httphttps://primes.utmt5k.eduorg/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a>
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Discussion
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| Mon Apr 03
| 10:36
| OEIS Server: https://oeis.org/edit/global/2966
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#7 by Russ Cox at Fri Mar 30 18:35:51 EDT 2012
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| AUTHOR
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_Michel Lagneau (mn.lagneau2(AT)orange.fr), _, Feb 22 2010
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Discussion
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| Fri Mar 30
| 18:35
| OEIS Server: https://oeis.org/edit/global/205
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#6 by Russ Cox at Fri Mar 30 17:35:02 EDT 2012
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| EXTENSIONS
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a(31)-a(38) from _Donovan Johnson (donovan.johnson(AT)yahoo.com), _, Jan 14 2012
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Discussion
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| Fri Mar 30
| 17:35
| OEIS Server: https://oeis.org/edit/global/163
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#5 by T. D. Noe at Sat Jan 14 13:44:05 EST 2012
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#4 by Michael B. Porter at Sat Jan 14 03:27:46 EST 2012
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#3 by Donovan Johnson at Sat Jan 14 02:12:07 EST 2012
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#2 by Donovan Johnson at Sat Jan 14 02:11:38 EST 2012
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| DATA
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1, 2, 3, 4, 6, 12, 16, 48, 64, 81, 162, 192, 270, 324, 750, 1029, 1296, 1512, 2058, 4096, 4116, 5184, 12288, 16464, 65536, 65856, 196608, 262144, 331776, 786432, 2100000, 4214784, 5308416, 21233664, 67436544, 269746176, 1073741824, 3221225472
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| EXTENSIONS
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a(31)-a(38) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 14 2012
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| STATUS
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approved
editing
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#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010
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| NAME
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Numbers n such that tau(sigma(n)) = rad(n)
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| DATA
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1, 2, 3, 4, 6, 12, 16, 48, 64, 81, 162, 192, 270, 324, 750, 1029, 1296, 1512, 2058, 4096, 4116, 5184, 12288, 16464, 65536, 65856, 196608, 262144, 331776, 786432
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| OFFSET
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1,2
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| COMMENTS
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rad(n) is the product of the primes dividing n (A007947 ) tau(n) is the number of divisors of n (A000005) sigma(n) is the sum of divisor of n (A000203).
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| LINKS
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C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=Tau">The Prime Glossary, Number of divisors</a>
W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>
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| FORMULA
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n such that A062068(n)= A007947(n)
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| EXAMPLE
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sigma(2) = 3, tau(3) = 2 and rad(2) = 2 sigma(65856) = 203200, tau(203200) = 42 and rad(65856) = 42
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| MAPLE
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with(numtheory):for n from 1 to 10000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)):if tau(sigma(n)) = t2 then print (n): else fi: od :
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| KEYWORD
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nonn
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| AUTHOR
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Michel Lagneau (mn.lagneau2(AT)orange.fr), Feb 22 2010
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| STATUS
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approved
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