cp's OEIS Frontend

A296134 Number of twice-factorizations of n of type (R,Q,R).

%I A296134 #16 Aug 07 2018 12:15:02
%S A296134 1,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,2,1,3,1,1,1,1,4,1,1,
%T A296134 1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,1,1,
%U A296134 1,1,1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1
%N A296134 Number of twice-factorizations of n of type (R,Q,R).
%C A296134 a(n) is the number of ways to choose a strict integer partition of a divisor of A052409(n).
%H A296134 Antti Karttunen, <a href="/A296134/b296134.txt">Table of n, a(n) for n = 1..65537</a>
%H A296134 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A296134 From _Antti Karttunen_, Jul 31 2018: (Start)
%F A296134 a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} A000009(d).
%F A296134 a(n) = A047966(A052409(n)). (End)
%e A296134 The a(16) = 4 twice-factorizations: (2)*(2*2*2), (2*2*2*2), (4*4), (16).
%t A296134 Table[DivisorSum[GCD@@FactorInteger[n][[All,2]],PartitionsQ],{n,100}]
%o A296134 (PARI)
%o A296134 A000009(n,k=(n-!(n%2))) = if(!n,1,my(s=0); while(k >= 1, if(k<=n, s += A000009(n-k,k)); k -= 2); (s));
%o A296134 A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
%o A296134 A296134(n) = if(1==n,n,sumdiv(A052409(n),d,A000009(d))); \\ _Antti Karttunen_, Jul 29 2018
%Y A296134 Cf. A000005, A000009, A001055, A047966, A047968, A052409, A052410, A089723, A281113, A295923, A295924, A295931, A295935, A296133.
%K A296134 nonn
%O A296134 1,4
%A A296134 _Gus Wiseman_, Dec 05 2017
%E A296134 More terms from _Antti Karttunen_, Jul 29 2018