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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Examples

			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)
		

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.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

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).

Programs

Mathematica

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

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

Formula

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