A003334 Numbers that are the sum of 11 positive cubes.

11, 18, 25, 32, 37, 39, 44, 46, 51, 53, 58, 60, 63, 65, 67, 70, 72, 74, 77, 79, 81, 84, 86, 88, 89, 91, 93, 95, 96, 98, 100, 102, 103, 105, 107, 109, 110, 112, 114, 115, 116, 117, 119, 121, 122, 123, 124, 126, 128, 129, 130, 131, 133, 135, 136, 137, 138, 140, 141, 142, 143, 144

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

As the order of addition doesn't matter we can assume terms are in nondecreasing order. - David A. Corneth, Aug 01 2020

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

Examples

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

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

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

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

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

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

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

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

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

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

Programs

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

Formula

a(n) = n + 92 for all n > 229. - M. F. Hasler, Aug 25 2020