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A325034
Sum of products of the multisets of prime indices of each prime index of n.
10
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
1,4
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.
FORMULA
Totally additive with a(prime(n)) = A003963(n).
EXAMPLE
94 has prime indices {1,15} with prime indices {{},{2,3}} with products {1,6} with sum a(94) = 7.
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Plus@@Times@@@primeMS/@primeMS[n], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 25 2019
STATUS
approved