cp's OEIS Frontend

A320655 Number of factorizations of n into semiprimes. Number of multiset partitions of the multiset of prime factors of n, into pairs.

%I A320655 #13 Jan 18 2021 06:22:59
%S A320655 1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0,1,1,
%T A320655 1,2,0,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0,1,1,1,1,1,0,2,0,1,0,1,1,0,0,0,
%U A320655 1,0,0,0,0,1,0,0,1,0,0,0,1,1,0,2,1,1,1,1,0,2,1,0,1,1,1,1,0,0,0,2,0,0,0,1,0
%N A320655 Number of factorizations of n into semiprimes. Number of multiset partitions of the multiset of prime factors of n, into pairs.
%C A320655 The characteristic function of nonzero terms is A065043. - _R. J. Mathar_, Jan 18 2021
%H A320655 Antti Karttunen, <a href="/A320655/b320655.txt">Table of n, a(n) for n = 1..65537</a>
%e A320655 The a(900) = 5 factorizations into semiprimes:
%e A320655   900 = (4*9*25)
%e A320655   900 = (4*15*15)
%e A320655   900 = (6*6*25)
%e A320655   900 = (6*10*15)
%e A320655   900 = (9*10*10)
%e A320655 The a(900) = 5 multiset partitions into pairs:
%e A320655   {{1,1},{2,2},{3,3}}
%e A320655   {{1,1},{2,3},{2,3}}
%e A320655   {{1,2},{1,2},{3,3}}
%e A320655   {{1,2},{1,3},{2,3}}
%e A320655   {{2,2},{1,3},{1,3}}
%t A320655 semfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[semfacs[n/d],Min@@#>=d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]==2&]}]];
%t A320655 Table[Length[semfacs[n]],{n,100}]
%o A320655 (PARI) A320655(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A320655(n/d, d))); (s)); \\ _Antti Karttunen_, Dec 06 2020
%Y A320655 The positions of zeros are A026424.
%Y A320655 Cf. A001055, A001222, A001358, A007716, A007717, A056239, A112798, A318871, A318953, A320462, A320656, A320658, A320659.
%K A320655 nonn
%O A320655 1,36
%A A320655 _Gus Wiseman_, Oct 18 2018
%E A320655 Data section extended up to 105 terms by _Antti Karttunen_, Dec 06 2020