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Numbers k such that the k-th partition number (A000041(k)) is a semiprime.
3

%I #21 Dec 11 2024 04:56:00

%S 7,8,12,23,65,67,76,81,87,90,92,93,95,121,123,143,146,161,181,203,218,

%T 220,235,241,251,252,287,321,330,388,406,423,437,438,443,455,456,507,

%U 555,594,603,626,646,661,665,672,685,707,708,715,720,755,808,837,856

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

%H Harry J. Smith, <a href="/A065729/b065729.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="http://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>

%e The 808th partition number 8151756509675604512522473567 = 5963320232189 * 1366982853893003.

%t Select[Range[900],PrimeOmega[PartitionsP[#]]==2&] (* _Harvey P. Dale_, Nov 27 2024 *)

%o (PARI) isok(k) = { bigomega(numbpart(k))==2 } \\ _Harry J. Smith_, Oct 28 2009

%Y Cf. A000041, A001358, A049575, A065728.

%K nonn,changed

%O 1,1

%A _Patrick De Geest_, Nov 18 2001

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

%E Missing a(38) = 507 added by _Harry J. Smith_, Oct 28 2009