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%I #7 Mar 27 2019 18:55:05
%S 1,1,2,2,1,3,3,2,4,3,2,4,4,1,4,5,3,4,4,3,6,5,2,5,4,4,4,6,3,7,5,2,6,8,
%T 4,5,6,4,6,6,1,9,8,4,5,6,5,6,6,3,7,6,4,6,10,4,6,8,3,8,9,6,8,11,5,5,6,
%U 2,7,8,5,9,8,4,7,6,4,10,12,4,8,9,6,8,9,3
%N Product of sums of the multisets of prime indices of each prime index of 2 * n + 1.
%C 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.
%F Fully multiplicative with a(prime(n)) = A056239(n), restricted to odd n.
%e 91 has prime indices {4,6} with prime indices {{1,1},{1,2}} with sums {2,3} with product a(45) = 6.
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Table[Times@@Plus@@@primeMS/@primeMS[n],{n,1,200,2}]
%Y Cf. A000720, A001055, A001222, A003963, A056239, A112798, A302242, A318949.
%Y Cf. A324926, A325031, A325032, A325033, A325034.
%K nonn
%O 0,3
%A _Gus Wiseman_, Mar 25 2019
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