A057904 Positive integers that are not the sum of exactly three positive cubes.

1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Differs from A047318 = numbers not congruent to 3 modulo 7: for example, A047318(26) = 29 is not in this sequence. - M. F. Hasler, Jun 30 2025

Examples

			3 = 1^3 + 1^3 + 1^3, therefore 3 is not in this sequence. Similarly,
10 = 1^3 + 1^3 + 2^3, therefore 10 is not in this sequence.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Cubic Number.

Crossrefs

Cf. A003072 (complement).

Cf. A047318 (not congruent to 3 mod 7), A308065 (not the same).

Programs

Mathematica

Select[Range[100], Count[ PowersRepresentations[#, 3, 3], pr_List /; FreeQ[pr, 0]] == 0 &] (* Jean-François Alcover, Oct 31 2012 *)

PARI

select( {is_A057904(n)=n<3 || !for(c=sqrtnint(n\/3,3),sqrtnint(n-2,3), isA003325(n-c^3)&&return)}, [1..99]) \\ M. F. Hasler, Jun 30 2025

Formula

A025456(a(n)) = 0. - Reinhard Zumkeller, Apr 23 2009