%I #34 Apr 24 2023 12:12:08

%S 9,16,23,30,35,37,42,44,49,51,56,58,61,63,65,68,70,72,75,77,79,82,84,

%T 86,87,89,91,93,94,96,98,100,101,103,105,107,108,110,112,113,114,115,

%U 119,120,121,122,124,126,127,128,129,131,133,134,135,138,139,140,141,142,145,146,147

%N Numbers that are the sum of 9 positive cubes.

%C 422 and 471 are the two largest of only 114 positive integers not in this sequence. This can be proved by induction. - _M. F. Hasler_, Aug 13 2020

%H David A. Corneth, <a href="/A003332/b003332.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H OEIS Wiki, <a href="/wiki/Index_to_Sums_of_like_powers">Index to sequences related to sums of like powers</a>.

%F a(n) = 114 + n for all n > 357. - _M. F. Hasler_, Aug 13 2020

%e From _David A. Corneth_, Aug 01 2020: (Start)

%e 1352 is in the sequence as 1352 = 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 6^3 + 6^3 + 8^3.

%e 2312 is in the sequence as 2312 = 5^3 + 5^3 + 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 7^3 + 8^3.

%e 3383 is in the sequence as 3383 = 4^3 + 5^3 + 5^3 + 5^3 + 6^3 + 6^3 + 8^3 + 10^3 + 10^3. (End)

%t With[{upto=150},Select[Union[Total/@Tuples[Range[Floor[Surd[upto-8,3]]]^3, 9]],#<=upto&]](* _Harvey P. Dale_, Jan 04 2015 *)

%o (PARI) (A003332_upto(N, k=9, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(160) \\ See also A003333 for alternate code. - _M. F. Hasler_, Aug 02 2020

%o A003332(n)=if(n>357, n+114, A003332_upto(471)[n]) \\ _M. F. Hasler_, Aug 13 2020

%Y Cf. numbers that are the sum of x nonzero y-th powers:

%Y A000404 (x=2, y=2), A000408 (3, 2), A000414 (4, 2), A047700 (5, 2),

%Y A003325 (2, 3), A003072 (3, 3), A003327 .. A003335 (4 .. 12, 3),

%Y A003336 .. A003346 (2 .. 12, 4), A003347 .. A003357 (2 .. 12, 5),

%Y A003358 .. A003368 (2 .. 12, 6), A003369 .. A003379 (2 .. 12, 7),

%Y A003380 .. A003390 (2 .. 12, 8), A003391 .. A004801 (2 .. 12, 9),

%Y A004802 .. A004812 (2 .. 12, 10), A004813 .. A004823 (2 .. 12, 11).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_