%I #5 Jun 29 2021 11:19:52

%S 1,2,3,4,5,6,8,44

%N Integers e such that each of q-1, q + sqrt(2*q) + 1 and q - sqrt(2*q) + 1 are either a power of prime or a semiprime, where q = 2^(2*e+1).

%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 (c) pp. 3-4.

%o (PARI) isor(q) = (q==1) || isprimepower(q) || (bigomega(q)==2);

%o isokc(e) = my(q=2^(2*e+1)); isor(q-1) && isor(q+sqrtint(2*q)+1) && isor(q-sqrtint(2*q)+1);

%Y Cf. A000961, A001358.

%Y Cf. A345898, A345899.

%K nonn,hard,more

%O 1,2

%A _Michel Marcus_, Jun 29 2021