cp's OEIS Frontend

A327523 Number of factorizations of the n-th number with distinct prime multiplicities A130091(n) into numbers > 1 with distinct prime multiplicities.

%I A327523 #4 Sep 16 2019 12:39:25
%S A327523 1,1,1,2,1,1,3,2,1,3,1,5,1,3,1,3,1,5,2,3,3,1,1,7,1,5,1,1,3,3,1,9,2,3,
%T A327523 3,1,5,5,1,1,3,11,1,3,1,11,1,3,3,1,9,5,1,5,1,3,14,1,3,3,1,1,5,1,11,1,
%U A327523 9,1,3,3,2,3,3,1,15,1,5,5,1,1,20,3,3,1,1
%N A327523 Number of factorizations of the n-th number with distinct prime multiplicities A130091(n) into numbers > 1 with distinct prime multiplicities.
%C A327523 A number's prime multiplicities are also called its (unsorted) prime signature.
%H A327523 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A327523 The a(57) = 14 factorizations of 96 together with the corresponding multiset partitions of {1,1,1,1,1,2}:
%e A327523   (2*2*2*2*2*3)  {{1}{1}{1}{1}{1}{2}}
%e A327523   (2*2*2*3*4)    {{1}{1}{1}{2}{11}}
%e A327523   (2*2*2*12)     {{1}{1}{1}{112}}
%e A327523   (2*2*3*8)      {{1}{1}{2}{111}}
%e A327523   (2*2*24)       {{1}{1}{1112}}
%e A327523   (2*3*4*4)      {{1}{2}{11}{11}}
%e A327523   (2*3*16)       {{1}{2}{1111}}
%e A327523   (2*4*12)       {{1}{11}{112}}
%e A327523   (2*48)         {{1}{11112}}
%e A327523   (3*4*8)        {{2}{11}{111}}
%e A327523   (3*32)         {{2}{11111}}
%e A327523   (4*24)         {{11}{1112}}
%e A327523   (8*12)         {{111}{112}}
%e A327523   (96)           {{111112}}
%t A327523 nn=100;
%t A327523 facsusing[s_,n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facsusing[Select[s,Divisible[n/d,#]&],n/d],Min@@#>=d&]],{d,Select[s,Divisible[n,#]&]}]];
%t A327523 y=Select[Range[nn],UnsameQ@@Last/@FactorInteger[#]&];
%t A327523 Table[Length[facsusing[Rest[y],n]],{n,y}]
%Y A327523 See link for additional cross-references.
%Y A327523 Cf. A098859, A112798, A130091, A255231.
%K A327523 nonn
%O A327523 1,4
%A A327523 _Gus Wiseman_, Sep 16 2019