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Composite numbers that have no "safe prime" factors.
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%I #20 Mar 17 2022 13:50:53

%S 4,6,8,9,12,16,18,24,26,27,32,34,36,38,39,48,51,52,54,57,58,62,64,68,

%T 72,74,76,78,81,82,86,87,93,96,102,104,106,108,111,114,116,117,122,

%U 123,124,128,129,134,136,142,144,146,148,152,153,156,158,159,162,164,169,171

%N Composite numbers that have no "safe prime" factors.

%C A350705 is a subsequence.

%H Karl-Heinz Hofmann, <a href="/A350706/b350706.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (Python)

%o from sympy import primefactors, isprime

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

%Y Cf. A350704, A350705, A005385.

%K nonn

%O 1,1

%A _Karl-Heinz Hofmann_, Feb 20 2022