A003330 Numbers that are the sum of 7 positive cubes.

7, 14, 21, 28, 33, 35, 40, 42, 47, 49, 54, 56, 59, 61, 66, 68, 70, 73, 75, 77, 80, 84, 85, 87, 91, 92, 94, 96, 98, 99, 103, 105, 106, 110, 111, 112, 113, 117, 118, 122, 124, 125, 129, 131, 132, 133, 136, 137, 138, 140, 143, 144, 145, 147, 148, 150, 151, 152, 154

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 increasing order. - David A. Corneth, Aug 01 2020

2408 is the largest among only 208 positive integers not in this sequence: cf. formula. - M. F. Hasler, Aug 23 2020

Examples

			From _M. F. Hasler_, Aug 23 2020: (Start)
The first few terms are multiples of 7 because of the coincidence that 2^3 - 1^3 = 7, equal to the number of cubes we consider here:
7 = 1^3 * 7 is the smallest sum of seven positive cubes.
14 = 1^3 * 6 + 2^3 = 6 + 8 is the next larger sum of seven positive cubes.
21 = 1^3 * 5 + 2^3 * 2 = 5 + 16 is the next larger sum of seven positive cubes.
28 = 1^3 * 4 + 2^3 * 3 = 4 + 24 is the next larger sum of seven positive cubes.
There are three more terms of this form, but the next larger sum of seven positive cubes is a(5) = 3^3 + 6 * 1^3 = 33. (End)
From _David A. Corneth_, Aug 01 2020: (Start)
2070 is in the sequence as 2070 = 4^3 + 4^3 + 4^3 + 5^3 + 8^3 + 8^3 +  9^3.
2383 is in the sequence as 2383 = 3^3 + 5^3 + 5^3 + 6^3 + 6^3 + 7^3 + 11^3.
3592 is in the sequence as 3592 = 4^3 + 5^3 + 6^3 + 9^3 + 9^3 + 9^3 + 10^3. (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).
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A004829, A003331, A003341.

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

PARI

(A003330_upto(N, k=7, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(160) \\ M. F. Hasler, Aug 02 2020

Formula

a(n) = n + 208 for all n > 2200. - M. F. Hasler, Aug 23 2020

Extensions

More terms from Arlin Anderson (starship1(AT)gmail.com)