

A162730


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


2



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 n1. Semiprimes n = pq with primes p < q such that p1 divides q1. 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]); (q1) % (p1) == 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



