cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A065729 #22 Feb 16 2025 08:32:45
%S A065729 7,8,12,23,65,67,76,81,87,90,92,93,95,121,123,143,146,161,181,203,218,
%T A065729 220,235,241,251,252,287,321,330,388,406,423,437,438,443,455,456,507,
%U A065729 555,594,603,626,646,661,665,672,685,707,708,715,720,755,808,837,856
%N A065729 Numbers k such that the k-th partition number (A000041(k)) is a semiprime.
%H A065729 Harry J. Smith, <a href="/A065729/b065729.txt">Table of n, a(n) for n = 1..100</a>
%H A065729 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm">Factorization results</a>
%H A065729 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%e A065729 The 808th partition number 8151756509675604512522473567 = 5963320232189 * 1366982853893003.
%t A065729 Select[Range[900],PrimeOmega[PartitionsP[#]]==2&] (* _Harvey P. Dale_, Nov 27 2024 *)
%o A065729 (PARI) isok(k) = { bigomega(numbpart(k))==2 } \\ _Harry J. Smith_, Oct 28 2009
%Y A065729 Cf.  A000041, A001358, A049575, A065728.
%K A065729 nonn
%O A065729 1,1
%A A065729 _Patrick De Geest_, Nov 18 2001
%E A065729 Offset changed from 0 to 1 by _Harry J. Smith_, Oct 28 2009
%E A065729 Missing a(38) = 507 added by _Harry J. Smith_, Oct 28 2009