A003332 Numbers that are the sum of 9 positive cubes.

9, 16, 23, 30, 35, 37, 42, 44, 49, 51, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 79, 82, 84, 86, 87, 89, 91, 93, 94, 96, 98, 100, 101, 103, 105, 107, 108, 110, 112, 113, 114, 115, 119, 120, 121, 122, 124, 126, 127, 128, 129, 131, 133, 134, 135, 138, 139, 140, 141, 142, 145, 146, 147

Offset

1,1

Comments

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

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

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

Formula

a(n) = 114 + n for all n > 357. - M. F. Hasler, Aug 13 2020

Example

From David A. Corneth, Aug 01 2020: (Start)
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.
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.
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)

Mathematica

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

Prog

(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
A003332(n)=if(n>357, n+114, A003332_upto(471)[n]) \\ M. F. Hasler, Aug 13 2020

Crossrefs

Cf. 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: A134256 A199859 A046463 * A345793 A091571 A225231

Adjacent sequences: A003329 A003330 A003331 * A003333 A003334 A003335

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved