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

5, 13, 17, 25, 29, 37, 41, 50, 53, 61, 65, 73, 75, 85, 89, 97, 101, 109, 113, 125, 130, 137, 145, 149, 157, 169, 170, 173, 175, 181, 185, 193, 195, 197, 205, 221, 229, 233, 241, 250, 255, 257, 265, 269, 275, 277, 281, 289, 290, 293, 305, 313, 317, 325, 337

Offset: 1

Author

Clark Kimberling, Jan 30 2025

Keywords

• nonn

Examples

			50 appears because 2*5*5 has 2 Pythagorean prime factors but only 1 non-Pythagorean prime factor.
		

Crossrefs

Cf. A000040, A002144, A002145, A083025, A376961, A377625, A378137, A378139, A378140.

Programs

Mathematica

f[{x_, y_}] := If[Mod[x, 4] == 1, y, -y];
s[n_] := Map[f, FactorInteger[n]];
p[n_] := {Total[Select[s[n], # > 0 &]], -Total[Select[s[n], # < 0 &]]};
p[1] = {0, 0};
t = Table[p[n], {n, 1, 500}];
u = Map[First, t];  (* A083025 *)
v = Map[Last, t] ;  (* A376961 *)
v - u (* A377625 *);
Flatten[Position[v - u, -1]]  (* this sequence *)