%I #20 Feb 16 2025 08:32:45

%S 15,22,77,1255,2012558,2679689,9289091,18004327,38887673,56634173,

%T 72533807,82010177,104651419,2056148051,2552338241,20390982757,

%U 27517052599,118159068427,749474411781,5134205287973,18028182516671

%N Partition numbers (A000041) that are semiprimes (A001358).

%C _Enoch Haga_ asks if this is a finite sequence. The larger these numbers get, the more opportunity for more factors.

%H Harry J. Smith, <a href="/A065728/b065728.txt">Table of n, a(n) for n=1,...,100</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm">Factorization results</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>

%F A064911(a(n))*A167392(a(n)) = 1. [From _Reinhard Zumkeller_, Nov 03 2009]

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

%t Select[PartitionsP[Range[0,450]],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Sep 19 2016 *)

%o (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

%Y Intersection of A001358 and A000041.

%Y Cf. A049575, A065729.

%K nonn,changed

%O 1,1

%A _Patrick De Geest_, Nov 18 2001

%E OFFSET changed from 0,1 to 1,1 by _Harry J. Smith_, Oct 28 2009