A325034 Sum of products of the multisets of prime indices of each prime index of n.

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

Offset: 1

Author

Gus Wiseman, Mar 25 2019

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

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

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

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[Plus@@Times@@@primeMS/@primeMS[n],{n,100}]

Formula

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