A350706 Composite numbers that have no "safe prime" factors.

4, 6, 8, 9, 12, 16, 18, 24, 26, 27, 32, 34, 36, 38, 39, 48, 51, 52, 54, 57, 58, 62, 64, 68, 72, 74, 76, 78, 81, 82, 86, 87, 93, 96, 102, 104, 106, 108, 111, 114, 116, 117, 122, 123, 124, 128, 129, 134, 136, 142, 144, 146, 148, 152, 153, 156, 158, 159, 162, 164, 169, 171

Offset: 1

Author

Karl-Heinz Hofmann, Feb 20 2022

Keywords

• nonn

Comments

A350705 is a subsequence.

Examples

			a(5) = 12 = 2 * 2 * 3 and {2, 3} are not in A005385.
		

Links

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

Crossrefs

Cf. A350704, A350705, A005385.

Programs

Mathematica

Select[Range[200], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[(#1 - 1)/2] &] &] (* Amiram Eldar, Feb 20 2022 *)

PARI

isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime((x-1)\2), factor(m)[, 1]));

Python

from sympy import primefactors, isprime
print([n for n in range(4, 172) if not isprime(n) and all(not isprime((p-1)//2) for p in primefactors(n))])