A302359 Numbers that are the sum of 3 squares > 1.

12, 17, 22, 24, 27, 29, 33, 34, 36, 38, 41, 43, 44, 45, 48, 49, 50, 54, 56, 57, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 74, 75, 76, 77, 78, 81, 82, 83, 84, 86, 88, 89, 90, 93, 94, 96, 97, 98, 99, 101, 102, 104, 105, 106, 107, 108, 109, 110, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 125, 126, 129

Offset: 1

Author

Ilya Gutkovskiy, Apr 06 2018

Keywords

• nonn

Examples

			33 is in the sequence because 33 = 2^2 + 2^2 + 5^2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000378, A000408, A085989, A214514, A281155.

Programs

Mathematica

max = 130; f[x_] := Sum[x^(k^2), {k, 2, 20}]^3; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, max}]]
With[{nn=15},Select[Union[Total/@Tuples[Range[2,nn]^2,3]],#<=nn^2+8&]] (* Harvey P. Dale, Jul 05 2021 *)

Python

from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(N):
    sqrs = list(takewhile(lambda x: x<=N, (i**2 for i in count(2))))
    sum3 = set(sum(c) for c in mc(sqrs, 3) if sum(c) <= N)
    return sorted(sum3)
print(aupto(129)) # Michael S. Branicky, Dec 17 2021