cp's OEIS Frontend

A327520 Number of factorizations of the n-th stable number A316476(n) into stable numbers > 1.

%I A327520 #6 Sep 16 2019 12:39:08
%S A327520 1,1,2,1,1,3,2,1,1,2,5,1,1,1,2,3,1,1,7,2,2,1,1,1,4,1,2,2,1,2,1,1,11,1,
%T A327520 2,1,1,4,2,1,5,1,2,1,2,2,2,1,4,1,1,1,1,1,2,2,2,3,1,15,1,7,1,1,2,2,2,1,
%U A327520 1,4,2,1,2,1,5,1,2,1,4,2,1,1,2,1,1,1
%N A327520 Number of factorizations of the n-th stable number A316476(n) into stable numbers > 1.
%C A327520 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476.
%H A327520 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 A327520 The a(26) = 4 factorizations of 45 into stable numbers:
%e A327520   (3*3*5)
%e A327520   (3*15)
%e A327520   (5*9)
%e A327520   (45)
%e A327520 The a(201) = 11 multiset partitions of the prime indices of 495 into stable multisets:
%e A327520   {{2},{2},{3},{5}}
%e A327520   {{2},{2},{3,5}}
%e A327520   {{2},{3},{2,5}}
%e A327520   {{2},{5},{2,3}}
%e A327520   {{2},{2,3,5}}
%e A327520   {{3},{2,2},{5}}
%e A327520   {{3},{2,2,5}}
%e A327520   {{2,2},{3,5}}
%e A327520   {{5},{2,2,3}}
%e A327520   {{2,3},{2,5}}
%e A327520   {{2,2,3,5}}
%t A327520 nn=100;
%t A327520 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 A327520 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A327520 y=Select[Range[nn],stableQ[PrimePi/@First/@FactorInteger[#],Divisible]&];
%t A327520 Table[Length[facsusing[Rest[y],n]],{n,y}]
%Y A327520 See link for additional cross-references.
%Y A327520 Cf. A001055, A303362, A305149.
%K A327520 nonn
%O A327520 1,3
%A A327520 _Gus Wiseman_, Sep 15 2019