A325034 - OEIS

%I #6 Mar 26 2019 21:05:37

%S 0,1,1,2,2,2,1,3,2,3,3,3,2,2,3,4,4,3,1,4,2,4,4,4,4,3,3,3,3,4,5,5,4,5,

%T 3,4,2,2,3,5,6,3,4,5,4,5,6,5,2,5,5,4,1,4,5,4,2,4,7,5,4,6,3,6,4,5,8,6,

%U 5,4,3,5,8,3,5,3,4,4,5,6,4,7,9,4,6,5,4

%N Sum of products of the multisets of prime indices of each prime index of n.

%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 Totally additive with a(prime(n)) = A003963(n).

%e 94 has prime indices {1,15} with prime indices {{},{2,3}} with products {1,6} with sum a(94) = 7.

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Table[Plus@@Times@@@primeMS/@primeMS[n],{n,100}]

%Y Cf. A000720, A001055, A001222, A003963, A056239, A066739, A112798, A302242.

%Y Cf. A324926, A325031, A325032, A325033, A325035.

%K nonn

%O 1,4

%A _Gus Wiseman_, Mar 25 2019