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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). 0

%I #10 Aug 29 2022 10:30:05

%S 15,35,39,45,51,55,75,87,91,95,105,111,115,117,119,123,135,143,153,

%T 155,159,165,175,183,187,195,203,215,219,225,235,245,247,255,259,261,

%U 267,273,275,285,287,291,295,299,303,315,319,323,327,333,335,339,345,351

%N 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).

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

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

%t Select[Range[1, 351, 2], Length[Union[Mod[FactorInteger[#][[;; , 1]], 4]]] == 2 &] (* _Amiram Eldar_, Aug 28 2022 *)

%o (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

%Y Cf. A004613, A004614.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Aug 27 2022

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Last modified September 14 03:39 EDT 2024. Contains 375911 sequences. (Running on oeis4.)