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.

A065728 Partition numbers (A000041) that are semiprimes (A001358).

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%I A065728 #20 Feb 16 2025 08:32:45
%S A065728 15,22,77,1255,2012558,2679689,9289091,18004327,38887673,56634173,
%T A065728 72533807,82010177,104651419,2056148051,2552338241,20390982757,
%U A065728 27517052599,118159068427,749474411781,5134205287973,18028182516671
%N A065728 Partition numbers (A000041) that are semiprimes (A001358).
%C A065728 _Enoch Haga_ asks if this is a finite sequence. The larger these numbers get, the more opportunity for more factors.
%H A065728 Harry J. Smith, <a href="/A065728/b065728.txt">Table of n, a(n) for n=1,...,100</a>
%H A065728 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm">Factorization results</a>
%H A065728 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime.</a>
%F A065728 A064911(a(n))*A167392(a(n)) = 1. [From _Reinhard Zumkeller_, Nov 03 2009]
%e A065728 E.g., the 808th partition number 8151756509675604512522473567 = 5963320232189 * 1366982853893003.
%t A065728 Select[PartitionsP[Range[0,450]],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Sep 19 2016 *)
%o A065728 (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 A065728 Intersection of A001358 and A000041.
%Y A065728 Cf. A049575, A065729.
%K A065728 nonn
%O A065728 1,1
%A A065728 _Patrick De Geest_, Nov 18 2001
%E A065728 OFFSET changed from 0,1 to 1,1 by _Harry J. Smith_, Oct 28 2009