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

Author

Patrick De Geest, Nov 18 2001

Keywords

• nonn

Comments

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

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n=1,...,100
• Hisanori Mishima, Factorization results
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Intersection of A001358 and A000041.

Cf. A049575, A065729.

Programs

Mathematica

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

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

Formula

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

Extensions

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