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%I #8 Jun 29 2021 11:20:03
%S 3,5,7,9,11,13,17,19,27,29,31,43,53,67,163,173,243,257,283,317,653,
%T 787,907,1867,2083,2187,2693,2803,3413,3643,3677,4253,4363,4373,4723,
%U 5443,5717,6197,6547,6653,8563,8573,9067,9187,9403,9643,10733,11443,11587,12163
%N Odd powers of primes q such that each of (q-1)/2 and (q+1)/2 is either a power of prime or a semiprime.
%H Peter J. Cameron, Pallabi Manna, and Ranjit Mehatari, <a href="https://arxiv.org/abs/2106.14217">On finite groups whose power graph is a cograph</a>, arXiv:2106.14217 [math.GR], 2021. See Theorem 1.3 (a) pp. 3-4.
%t q[n_] := n == 1 || PrimePowerQ[n] || PrimeOmega[n] == 2; Select[Range[3, 10^4, 2], PrimePowerQ[#] && q[(# - 1)/2] && q[(# + 1)/2] &] (* _Amiram Eldar_, Jun 29 2021 *)
%o (PARI) isor(q) = (q==1) || isprimepower(q) || (bigomega(q)==2);
%o isoka(q) = (q%2) && isprimepower(q) && isor((q-1)/2) && isor((q+1)/2);
%Y Cf. A000961, A001358.
%Y Cf. A345899, A345900.
%K nonn
%O 1,1
%A _Michel Marcus_, Jun 29 2021
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