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

1,1

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

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

OEIS Wiki, Index to sequences related to sums of like powers.

Formula

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

Example

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)

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 *)

Prog

(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

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).

Sequence in context: A070043 A003786 A008686 * A345783 A016993 A079043

Adjacent sequences: A003328 A003329 A003330 * A003332 A003333 A003334

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved