cp's OEIS Frontend

A327524 Number of factorizations of the n-th uniform number A072774(n) into uniform numbers > 1.

%I A327524 #6 Sep 18 2019 04:57:08
%S A327524 1,1,1,2,1,2,1,3,2,2,1,1,2,2,5,1,1,2,2,1,2,2,3,1,5,1,7,2,2,2,7,1,2,2,
%T A327524 1,5,1,2,1,2,2,1,2,2,2,1,1,2,11,2,5,1,2,5,1,1,2,2,5,1,5,2,1,2,2,2,1,2,
%U A327524 2,2,2,1,7,1,5,1,5,2,1,1,5,2,1,5,2,2,2
%N A327524 Number of factorizations of the n-th uniform number A072774(n) into uniform numbers > 1.
%C A327524 A number is uniform if its prime multiplicities are all equal, meaning it is a power of a squarefree number. Uniform numbers are listed in A072774.
%H A327524 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 A327524 The a(31) = 7 factorizations of 36 into uniform numbers together with the corresponding multiset partitions of {1,1,2,2}:
%e A327524   (2*2*3*3)  {{1},{1},{2},{2}}
%e A327524   (2*2*9)    {{1},{1},{2,2}}
%e A327524   (2*3*6)    {{1},{2},{1,2}}
%e A327524   (3*3*4)    {{2},{2},{1,1}}
%e A327524   (4*9)      {{1,1},{2,2}}
%e A327524   (6*6)      {{1,2},{1,2}}
%e A327524   (36)       {{1,1,2,2}}
%t A327524 nn=100;
%t A327524 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 A327524 y=Select[Range[nn],SameQ@@Last/@FactorInteger[#]&];
%t A327524 Table[Length[facsusing[Rest[y],n]],{n,y}];
%Y A327524 See link for additional cross-references.
%Y A327524 Cf. A000961, A001055, A005117, A007947, A071625, A112798.
%K A327524 nonn
%O A327524 1,4
%A A327524 _Gus Wiseman_, Sep 17 2019