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
Keywords
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
Programs
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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