A326567 Numerator of the average of the multiset of prime indices of n.

1, 2, 1, 3, 3, 4, 1, 2, 2, 5, 4, 6, 5, 5, 1, 7, 5, 8, 5, 3, 3, 9, 5, 3, 7, 2, 2, 10, 2, 11, 1, 7, 4, 7, 3, 12, 9, 4, 3, 13, 7, 14, 7, 7, 5, 15, 6, 4, 7, 9, 8, 16, 7, 4, 7, 5, 11, 17, 7, 18, 6, 8, 1, 9, 8, 19, 3, 11, 8, 20, 7, 21, 13, 8, 10, 9, 3, 22, 7, 2, 7

Offset: 2

Author

Gus Wiseman, Jul 13 2019

Keywords

• nonn
• frac

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

			The prime indices of 12 are {1,1,2}, with average 4/3, so a(12) = 4.
		

Crossrefs

Cf. A001222, A001414, A056239, A067629, A112798, A123528/A123529, A289508, A289509, A290103, A316413, A326568.

Programs

Mathematica

Table[Numerator[Sum[q[[2]]*PrimePi[q[[1]]],{q,FactorInteger[n]}]/PrimeOmega[n]],{n,2,100}]