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

Author

Eric W. Weisstein

Keywords

• nonn

Comments

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

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

Crossrefs

Complement is A003327.

Programs

Mathematica

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

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