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

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A004613, A004614.

Sequence in context: A257591 A284406 A329589 * A154988 A345331 A360110

Adjacent sequences: A356791 A356792 A356793 * A356795 A356796 A356797

Keyword

nonn

Author

Jon E. Schoenfield, Aug 27 2022

Status

approved