A345900 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).

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

Offset

1,2

Links

Table of n, a(n) for n=1..8.

Peter J. Cameron, Pallabi Manna, and Ranjit Mehatari, On finite groups whose power graph is a cograph, arXiv:2106.14217 [math.GR], 2021. See Theorem 1.3 (c) pp. 3-4.

Prog

(PARI) isor(q) = (q==1) || isprimepower(q) || (bigomega(q)==2);
isokc(e) = my(q=2^(2*e+1)); isor(q-1) && isor(q+sqrtint(2*q)+1) && isor(q-sqrtint(2*q)+1);

Crossrefs

Cf. A000961, A001358.

Cf. A345898, A345899.

Sequence in context: A128421 A115885 A259390 * A029964 A368240 A275583

Adjacent sequences: A345897 A345898 A345899 * A345901 A345902 A345903

Keyword

nonn,hard,more

Author

Michel Marcus, Jun 29 2021

Status

approved