A345898 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.

3, 5, 7, 9, 11, 13, 17, 19, 27, 29, 31, 43, 53, 67, 163, 173, 243, 257, 283, 317, 653, 787, 907, 1867, 2083, 2187, 2693, 2803, 3413, 3643, 3677, 4253, 4363, 4373, 4723, 5443, 5717, 6197, 6547, 6653, 8563, 8573, 9067, 9187, 9403, 9643, 10733, 11443, 11587, 12163

Offset

1,1

Links

Table of n, a(n) for n=1..50.

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 (a) pp. 3-4.

Mathematica

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 *)

Prog

(PARI) isor(q) = (q==1) || isprimepower(q) || (bigomega(q)==2);
isoka(q) = (q%2) && isprimepower(q) && isor((q-1)/2) && isor((q+1)/2);

Crossrefs

Cf. A000961, A001358.

Cf. A345899, A345900.

Sequence in context: A050150 A062090 A358975 * A172095 A309361 A133854

Adjacent sequences: A345895 A345896 A345897 * A345899 A345900 A345901

Keyword

nonn

Author

Michel Marcus, Jun 29 2021

Status

approved