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A380657 Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).

%I A380657 #6 Jan 31 2025 13:42:02
%S A380657 5,13,17,25,29,37,41,50,53,61,65,73,75,85,89,97,101,109,113,125,130,
%T A380657 137,145,149,157,169,170,173,175,181,185,193,195,197,205,221,229,233,
%U A380657 241,250,255,257,265,269,275,277,281,289,290,293,305,313,317,325,337
%N A380657 Numbers whose prime factorization has more Pythagorean prime factors than non-Pythagorean prime factors (including multiplicities).
%e A380657 50 appears because 2*5*5 has 2 Pythagorean prime factors but only 1 non-Pythagorean prime factor.
%t A380657 f[{x_, y_}] := If[Mod[x, 4] == 1, y, -y];
%t A380657 s[n_] := Map[f, FactorInteger[n]];
%t A380657 p[n_] := {Total[Select[s[n], # > 0 &]], -Total[Select[s[n], # < 0 &]]};
%t A380657 p[1] = {0, 0};
%t A380657 t = Table[p[n], {n, 1, 500}];
%t A380657 u = Map[First, t];  (* A083025 *)
%t A380657 v = Map[Last, t] ;  (* A376961 *)
%t A380657 v - u (* A377625 *);
%t A380657 Flatten[Position[v - u, -1]]  (* this sequence *)
%Y A380657 Cf. A000040, A002144, A002145, A083025, A376961, A377625, A378137, A378139, A378140.
%K A380657 nonn
%O A380657 1,1
%A A380657 _Clark Kimberling_, Jan 30 2025