A350705 Composite numbers that have no Sophie Germain prime and no "safe prime" factors.

169, 221, 247, 289, 323, 361, 403, 481, 527, 559, 589, 629, 703, 731, 793, 817, 871, 923, 949, 961, 1027, 1037, 1139, 1147, 1159, 1207, 1241, 1261, 1273, 1313, 1333, 1339, 1343, 1349, 1369, 1387, 1417, 1501, 1591, 1649, 1651, 1717, 1751, 1781, 1807, 1843, 1849, 1853

Offset: 1

Author

Karl-Heinz Hofmann, Feb 14 2022

Keywords

• nonn

Comments

Prime factors of the terms have to be in A059500.

Examples

			a(2) = 221 = 13 * 17 and {13, 17} are neither in A005384 nor in A005385, but they are in A059500.
		

Links

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

Crossrefs

Subsequence of A350704 and A350706.

Cf. A005384, A005385, A053176, A059500.

Programs

Mathematica

Select[Range[2000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[2*#1 + 1] && ! PrimeQ[(#1 - 1)/2] &] &] (* Amiram Eldar, Feb 15 2022 *)

PARI

isok(m) = if ((m>1) && !isprime(m), my(f=factor(m)[,1]); !#select(x->isprime(2*x+1), f) && !#select(x->isprime((x-1)/2), f)); \\ Michel Marcus, Feb 14 2022

Python

from sympy import primefactors, isprime
print([n for n in range(2,1854) if not isprime(n) and all(not isprime(p*2+1) and not isprime((p-1)//2) for p in primefactors(n))])