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%I #24 Jul 29 2018 20:48:13
%S 1,1,1,3,1,1,1,4,3,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,3,1,4,1,1,1,1,8,1,1,
%T 1,3,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,17,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1
%N Number of twice-factorizations of n of type (R,P,R).
%C a(n) is the number of ways to choose an integer partition of a divisor of A052409(n).
%H Antti Karttunen, <a href="/A295924/b295924.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F a(1) = 1; for n > 1, a(n) = Sum_{d|A052409(n)} A000041(d). - _Antti Karttunen_, Jul 29 2018
%e The a(16) = 8 twice-factorizations are (2)*(2)*(2)*(2), (2)*(2)*(2*2), (2)*(2*2*2), (2*2)*(2*2), (2*2*2*2), (4)*(4), (4*4), (16).
%t Table[DivisorSum[GCD@@FactorInteger[n][[All,2]],PartitionsP],{n,100}]
%o (PARI)
%o A052409(n) = { my(k=ispower(n)); if(k, k, n>1); }; \\ From A052409
%o A295924(n) = if(1==n,n,sumdiv(A052409(n),d,numbpart(d))); \\ _Antti Karttunen_, Jul 29 2018
%Y Cf. A000005, A000041, A001055, A047968, A052409, A052410, A089723, A281113, A284639, A295923, A295931, A295935, A296134.
%K nonn
%O 1,4
%A _Gus Wiseman_, Nov 30 2017
%E More terms from _Antti Karttunen_, Jul 29 2018
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