A162730 - OEIS

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

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OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..59.

PROG

(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

CROSSREFS

Subsequence of A006881 (squarefree semiprimes).

Sequence in context: A201650 A201514 A201464 * A180074 A338905 A093772

Adjacent sequences: A162727 A162728 A162729 * A162731 A162732 A162733

KEYWORD

nonn

AUTHOR

Vassilis Papadimitriou, Jul 12 2009, Jul 13 2009

EXTENSIONS

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

STATUS

approved