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

1,2

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

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 307.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Eric Weisstein's World of Mathematics, Cubic Number.

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A003072 (complement).

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

Sequence in context: A183301 A308065 A047318 * A188397 A385455 A027925

Adjacent sequences: A057901 A057902 A057903 * A057905 A057906 A057907

Keyword

nonn

Author

Eric W. Weisstein

Status

approved