A162730 Semiprimes n = pq such that q = kp - k + 1, where p,q primes and k > 1.

6, 10, 14, 15, 21, 22, 26, 33, 34, 38, 39, 46, 51, 57, 58, 62, 65, 69, 74, 82, 85, 86, 87, 91, 93, 94, 106, 111, 118, 122, 123, 129, 133, 134, 141, 142, 145, 146, 158, 159, 166, 177, 178, 183, 185, 194, 201, 202, 205, 206, 213, 214, 217, 218, 219, 226, 237, 249, 254

Offset: 1

Author

Vassilis Papadimitriou, Jul 12 2009, Jul 13 2009

Keywords

• nonn

Comments

It seems that most of the semiprimes of this form (but not all, only those satisfying an additional property) can be factored very quickly (e.g. numbers with up to 1200 decimal digits can be factored in a couple of seconds) using a very simple method.

Squarefree semiprimes n such that lpf(n)-1 divides n-1. Semiprimes n = pq with primes p < q such that p-1 divides q-1. If n is such a semiprime, then q^n == q (mod n). - Thomas Ordowski, Sep 18 2018

Crossrefs

Subsequence of A006881 (squarefree semiprimes).

Programs

PARI

isok(n) = {if ((bigomega(n) == 2) && (omega(n) == 2), my(p = factor(n)[1, 1], q = factor(n)[2, 1]); (q-1) % (p-1) == 0;);} \\ Michel Marcus, Sep 18 2018

Extensions

More terms from R. J. Mathar, Aug 06 2009