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Numerator of the average of the multiset of prime indices of n.
120

%I #5 Jul 13 2019 09:13:27

%S 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,

%T 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,

%U 9,8,19,3,11,8,20,7,21,13,8,10,9,3,22,7,2,7

%N Numerator of the average of the multiset of prime indices 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.

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

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

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

%K nonn,frac

%O 2,2

%A _Gus Wiseman_, Jul 13 2019