A100829 Numbers that are a sum of two nonzero squares and not divisible by 17.

2, 5, 8, 10, 13, 18, 20, 25, 26, 29, 32, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 72, 73, 74, 80, 82, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 137, 145, 146, 148, 149, 157, 160, 162, 164, 169, 173, 178, 180, 181, 185, 193, 194, 197

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 06 2005

Keywords

• nonn

Crossrefs

Cf. A000404, A098365.

Programs

Maple

filter:= proc(x) local F;
  if x mod 17 = 0 then return false fi;
  F:= ifactors(x)[2];
  if ormap(t -> t[1] mod 4 = 3 and t[2]::odd, F) then return false fi;
  ormap(t -> t[1] mod 4 = 1 or (t[1]=2 and t[2]::odd), F)
end proc:
select(filter, [$1..200]); # Robert Israel, Jun 17 2025

Mathematica

With[{upto=200},Select[Total/@Tuples[Range[Ceiling[Sqrt[upto]]]^2,2], Mod[ #,17]!=0&&#<=upto&]]//Union (* Harvey P. Dale, May 18 2019 *)

Extensions

Definition corrected by Robert Israel, Jun 17 2025