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Numbers that are the sum of 11 positive cubes.
32

%I #23 Oct 21 2023 18:24:13

%S 11,18,25,32,37,39,44,46,51,53,58,60,63,65,67,70,72,74,77,79,81,84,86,

%T 88,89,91,93,95,96,98,100,102,103,105,107,109,110,112,114,115,116,117,

%U 119,121,122,123,124,126,128,129,130,131,133,135,136,137,138,140,141,142,143,144

%N Numbers that are the sum of 11 positive cubes.

%C As the order of addition doesn't matter we can assume terms are in nondecreasing order. - _David A. Corneth_, Aug 01 2020

%C The sequence contains all integers greater than 321 which is the last of only 92 positive integers not in this sequence. - _M. F. Hasler_, Aug 25 2020

%H David A. Corneth, <a href="/A003334/b003334.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%F a(n) = n + 92 for all n > 229. - _M. F. Hasler_, Aug 25 2020

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

%e 1120 is in the sequence as 1120 = 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 8^3.

%e 2339 is in the sequence as 2339 = 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 5^3 + 9^3 + 9^3.

%e 3594 is in the sequence as 3594 = 4^3 + 5^3 + 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 7^3 + 7^3 + 8^3 + 10^3. (End)

%o (PARI) (A003334_upto(N, k=11, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(150) \\ See also A003333 for alternate code. - _M. F. Hasler_, Aug 03 2020

%Y Other sequences S(k, m) of numbers that are the sum of k nonzero m-th powers:

%Y A000404 = S(2, 2), A000408 = S(3, 2), A000414 = S(4, 2) complement of A000534,

%Y A047700 = S(5, 2) complement of A047701, A180968 = complement of S(6,2);

%Y A003325 = S(2, 3), A003072 = S(3, 3), A003327 .. A003335 = S(4 .. 12, 3) and A332107 .. A332111 = complement of S(7 .. 11, 3);

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

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

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

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

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_