A046039 Numbers which cannot be represented as a sum of distinct 4th powers.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

Last term is a(889576) = 5134240. [Charles R Greathouse IV, Feb 26 2012]

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..60000
• Eric Weisstein's World of Mathematics, Biquadratic Number

Crossrefs

Cf. A001422, A001476. Complement of A003999.

Cf. A279487.

Programs

Mathematica

max = 2000; f[x_] := Product[1 + x^(k^4), {k, 1, 10}]; A003999 = Exponent[#, x]& /@ List @@ Normal[Series[f[x], {x, 0, max}]] // Rest; A046039 = Complement[Range[max], A003999][[1 ;; 71]](* Jean-François Alcover, Nov 09 2012, after Charles R Greathouse IV *)

PARI

select( is_A046039(n,m=n)={m^4>n&& m=sqrtnint(n,4); n!=m^4&& !while(m>1, is_A046039(n-m^4, m--)||return)}, [1..74]) \\ M. F. Hasler, Apr 21 2020