A057905 Positive integers that are not the sum of exactly four positive cubes.

1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 71, 72, 73, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87

Offset

1,2

Comments

It is conjectured that this sequence is finite, with 7373170279850 as its last member. - Charles R Greathouse IV, Jan 14 2017

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

Brennan Benfield and Oliver Lippard, Integers that are not the sum of positive powers, arXiv:2404.08193 [math.NT], 2024. p. 5.

Eric Weisstein's World of Mathematics, Cubic Number

Mathematica

pr[n_] := Select[ PowersRepresentations[n, 4, 3], FreeQ[#, 0] &]; Select[ Range[90], pr[#] == {} &] (* Jean-François Alcover, Nov 08 2012 *)

Prog

(PARI) list(lim)=my(v=List(), e=1+lim\1, x='x, t); t=sum(i=1, sqrtnint(e-4, 3), x^i^3, O(x^e))^4; for(n=1, lim, if(polcoeff(t, n)==0, listput(v, n))); Vec(v) \\ Charles R Greathouse IV, Jan 14 2017

Crossrefs

Complement is A003327.

Sequence in context: A029927 A047334 A032775 * A353084 A039253 A193533

Adjacent sequences: A057902 A057903 A057904 * A057906 A057907 A057908

Keyword

nonn

Author

Eric W. Weisstein

Status

approved