A003331 Numbers that are the sum of 8 positive cubes.

8, 15, 22, 29, 34, 36, 41, 43, 48, 50, 55, 57, 60, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 86, 88, 92, 93, 95, 97, 99, 100, 102, 104, 106, 107, 111, 112, 113, 114, 118, 119, 120, 121, 123, 125, 126, 130, 132, 133, 134, 137, 138, 139, 140, 141, 144, 145, 146, 148, 149

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

620 is the largest among only 142 positive integers not in this sequence. This can be proved by induction. - M. F. Hasler, Aug 13 2020

Examples

			From _David A. Corneth_, Aug 01 2020: (Start)
1796 is in the sequence as 1796 = 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 7^3 + 7^3 + 9^3.
2246 is in the sequence as 2246 = 2^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 7^3 + 11^3.
3164 is in the sequence as 3164 = 5^3 + 5^3 + 6^3 + 6^3 + 8^3 + 8^3 + 9^3 + 9^3.(End)
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• OEIS Wiki, Index to sequences related to sums of like powers.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Other sequences of numbers that are the sum of x nonzero y-th powers:

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

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

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

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

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

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

Programs

Mathematica

Module[{upto=200,c},c=Floor[Surd[upto,3]];Select[Union[Total/@ Tuples[ Range[ c]^3,8]],#<=upto&]] (* Harvey P. Dale, Jan 11 2016 *)

PARI

(A003331_upto(N, k=8, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(150) \\ M. F. Hasler, Aug 02 2020
A003331(n)=if(n>478, n+142, n>329, n+141, A003331_upto(470)[n]) \\ M. F. Hasler, Aug 13 2020

Python

from itertools import combinations_with_replacement as mc
def aupto(lim):
    cbs = (i**3 for i in range(1, int((lim-7)**(1/3))+2))
    return sorted(set(k for k in (sum(c) for c in mc(cbs, 8)) if k <= lim))
print(aupto(150)) # Michael S. Branicky, Aug 15 2021

Formula

a(n) = 142 + n for all n > 478. - M. F. Hasler, Aug 13 2020