A307217 Semiprimes p*q such that 2^(p+q) == 1 (mod p*q).

9, 15, 35, 119, 5543, 74447, 90859, 110767, 222179, 389993, 1526849, 2927297, 3626699, 4559939, 24017531, 137051711, 160832099, 229731743, 627699239, 880021141, 1001124539, 1041287603, 1104903617, 1592658611, 1717999139, 8843679683, 15575602979, 15614760199, 20374337479

Offset: 1

Author

Thomas Ordowski, Mar 29 2019

Keywords

• nonn

Comments

For k > 9, these are semiprimes k such that 2^(k+1) == 1 (mod k): semiprimes in A187787.

In this sequence, only 9 is a perfect square. - Jinyuan Wang, Mar 30 2019

Crossrefs

Cf. A001358, A046315, A127104, A187787, A208728.

Programs

PARI

isok(k) = (bigomega(k)==2) && (Mod(2, k)^(k+1) == 1); \\ (for k > 9) Michel Marcus, Mar 29 2019

Perl

use ntheory ":all"; forsemiprimes { print "$\n" if powmod(2, vecsum(factor($)), $) == 1 } 4, 1e7; # _Daniel Suteu, Mar 30 2019

Extensions

a(7)-a(18) from Amiram Eldar, Mar 29 2019

a(19)-a(29) from Daniel Suteu, Mar 29 2019