A356794 Odd numbers that have at least one prime factor congruent to 1 (mod 4) and at least one prime factor congruent to 3 (mod 4).

15, 35, 39, 45, 51, 55, 75, 87, 91, 95, 105, 111, 115, 117, 119, 123, 135, 143, 153, 155, 159, 165, 175, 183, 187, 195, 203, 215, 219, 225, 235, 245, 247, 255, 259, 261, 267, 273, 275, 285, 287, 291, 295, 299, 303, 315, 319, 323, 327, 333, 335, 339, 345, 351

Offset: 1

Author

Jon E. Schoenfield, Aug 27 2022

Keywords

• nonn

Comments

This sequence consists of the odd positive integers that are in neither A004613 nor A004614.

Examples

			15 is a term: its prime factors are 3 and 5; 3 == 3 (mod 4), 5 == 1 (mod 4).
		

Crossrefs

Cf. A004613, A004614.

Programs

Mathematica

Select[Range[1, 351, 2], Length[Union[Mod[FactorInteger[#][[;; , 1]], 4]]] == 2 &] (* Amiram Eldar, Aug 28 2022 *)

PARI

isok(m) = if (m % 2, my(vf=factor(m)[,1]); (#select(x->((x%4)==1), vf) >= 1) && (#select(x->((x%4)==3), vf) >= 1)); \\ Michel Marcus, Aug 29 2022