A350704 Composite numbers that have no Sophie Germain prime factors.

49, 91, 119, 133, 169, 217, 221, 247, 259, 289, 301, 323, 329, 343, 361, 403, 413, 427, 469, 481, 497, 511, 527, 553, 559, 589, 611, 629, 637, 679, 703, 707, 721, 731, 749, 763, 767, 793, 799, 817, 833, 871, 889, 893, 923, 931, 949, 959, 961, 973, 1003, 1027, 1037, 1043

Offset: 1

Author

Karl-Heinz Hofmann, Feb 11 2022

Keywords

• nonn

Comments

A157342 is a subsequence. First differs at a(14) = 343.

A350705 is a subsequence too.

Examples

			a(2) = 91 = 7 * 13 and {7, 13} are not in A005384.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A157342, A005384, A053176, A350705, A350706.

Programs

Mathematica

Select[Range[1000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], !PrimeQ[2*#1 + 1] &] &] (* Amiram Eldar, Feb 12 2022 *)

PARI

isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime(2*x+1), factor(m)[,1])); \\ Michel Marcus, Feb 11 2022

Python

from sympy import primefactors, isprime
print([n for n in range(2,1044) if not isprime(n) and all(not isprime(p*2+1) for p in primefactors(n))])