A325033 - OEIS

%I #5 Mar 26 2019 21:05:30

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

%T 4,2,4,3,4,2,6,3,5,3,4,4,5,1,4,4,5,3,4,3,5,2,4,4,7,3,5,5,4,0,5,4,8,4,

%U 5,4,5,2,6,4,5,3,5,4,6,2,4,6,9,3,6,5,5

%N Sum of sums 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)) = A056239(n).

%e 91 has prime indices {4,6} with prime indices {{1,1},{1,2}} with sum a(91) = 5.

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

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

%Y Cf. A000720, A056239, A109082, A112798, A302242.

%Y Cf. A324926, A325032, A325034, A325035.

%K nonn

%O 1,5

%A _Gus Wiseman_, Mar 25 2019