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

1,1

Links

Table of n, a(n) for n=1..55.

Example

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

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 *)

Crossrefs

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

Sequence in context: A126887 A339952 A087445 * A020882 A081804 A004613

Adjacent sequences: A380654 A380655 A380656 * A380658 A380659 A380660

Keyword

nonn

Author

Clark Kimberling, Jan 30 2025

Status

approved