A065728 Partition numbers (A000041) that are semiprimes (A001358).

15, 22, 77, 1255, 2012558, 2679689, 9289091, 18004327, 38887673, 56634173, 72533807, 82010177, 104651419, 2056148051, 2552338241, 20390982757, 27517052599, 118159068427, 749474411781, 5134205287973, 18028182516671

Offset

1,1

Comments

Enoch Haga asks if this is a finite sequence. The larger these numbers get, the more opportunity for more factors.

Links

Harry J. Smith, Table of n, a(n) for n=1,...,100

Hisanori Mishima, Factorization results

Eric Weisstein's World of Mathematics, Semiprime.

Formula

A064911(a(n))*A167392(a(n)) = 1. [From Reinhard Zumkeller, Nov 03 2009]

Example

E.g., the 808th partition number 8151756509675604512522473567 = 5963320232189 * 1366982853893003.

Mathematica

Select[PartitionsP[Range[0, 450]], PrimeOmega[#]==2&] (* Harvey P. Dale, Sep 19 2016 *)

Prog

(PARI) { n=0; for (m=1, 10^9, p=numbpart(m); if (bigomega(p) == 2, write("b065728.txt", n++, " ", p); if (n==100, return)) ) } \\ Harry J. Smith, Oct 28 2009

Crossrefs

Intersection of A001358 and A000041.

Cf. A049575, A065729.

Sequence in context: A018889 A186525 A236107 * A344134 A241253 A317793

Adjacent sequences: A065725 A065726 A065727 * A065729 A065730 A065731

Keyword

nonn

Author

Patrick De Geest, Nov 18 2001

Extensions

OFFSET changed from 0,1 to 1,1 by Harry J. Smith, Oct 28 2009

Status

approved