A065729 Numbers k such that the k-th partition number (A000041(k)) is a semiprime.

7, 8, 12, 23, 65, 67, 76, 81, 87, 90, 92, 93, 95, 121, 123, 143, 146, 161, 181, 203, 218, 220, 235, 241, 251, 252, 287, 321, 330, 388, 406, 423, 437, 438, 443, 455, 456, 507, 555, 594, 603, 626, 646, 661, 665, 672, 685, 707, 708, 715, 720, 755, 808, 837, 856

Offset: 1

Author

Patrick De Geest, Nov 18 2001

Keywords

• nonn

Examples

			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

Cf. A000041, A001358, A049575, A065728.

Programs

Mathematica

Select[Range[900],PrimeOmega[PartitionsP[#]]==2&] (* Harvey P. Dale, Nov 27 2024 *)

PARI

isok(k) = { bigomega(numbpart(k))==2 } \\ Harry J. Smith, Oct 28 2009

Extensions

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

Missing a(38) = 507 added by Harry J. Smith, Oct 28 2009