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%I #33 Mar 17 2022 13:52:34
%S 49,91,119,133,169,217,221,247,259,289,301,323,329,343,361,403,413,
%T 427,469,481,497,511,527,553,559,589,611,629,637,679,703,707,721,731,
%U 749,763,767,793,799,817,833,871,889,893,923,931,949,959,961,973,1003,1027,1037,1043
%N Composite numbers that have no Sophie Germain prime factors.
%C A157342 is a subsequence. First differs at a(14) = 343.
%C A350705 is a subsequence too.
%H Karl-Heinz Hofmann, <a href="/A350704/b350704.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 91 = 7 * 13 and {7, 13} are not in A005384.
%t Select[Range[1000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], !PrimeQ[2*#1 + 1] &] &] (* _Amiram Eldar_, Feb 12 2022 *)
%o (Python)
%o from sympy import primefactors, isprime
%o print([n for n in range(2,1044) if not isprime(n) and all(not isprime(p*2+1) for p in primefactors(n))])
%o (PARI) isok(m) = if ((m>1) && !isprime(m), !#select(x->isprime(2*x+1), factor(m)[,1])); \\ _Michel Marcus_, Feb 11 2022
%Y Cf. A157342, A005384, A053176, A350705, A350706.
%K nonn
%O 1,1
%A _Karl-Heinz Hofmann_, Feb 11 2022
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