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Numerator of the average of the set of distinct prime indices of n.
27

%I #7 Jul 15 2019 01:44:26

%S 1,2,1,3,3,4,1,2,2,5,3,6,5,5,1,7,3,8,2,3,3,9,3,3,7,2,5,10,2,11,1,7,4,

%T 7,3,12,9,4,2,13,7,14,3,5,5,15,3,4,2,9,7,16,3,4,5,5,11,17,2,18,6,3,1,

%U 9,8,19,4,11,8,20,3,21,13,5,9,9,3,22,2,2,7

%N Numerator of the average of the set of distinct 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 distinct prime indices of 12 are {1,2}, with average 3/2, so a(12) = 3.

%e The sequence of fractions begins: 1, 2, 1, 3, 3/2, 4, 1, 2, 2, 5, 3/2, 6, 5/2, 5/2, 1, 7, 3/2, 8, 2, 3, 3, 9, 3/2, 3, 7/2, 2, 5/2, 10, 2.

%t Table[Numerator[Mean[PrimePi/@First/@FactorInteger[n]]],{n,2,100}]

%Y The average of the multiset of prime indices is A326567/A326568.

%Y The average of the multiset of prime factors is A123528/A123529.

%Y The average of the set of distinct prime indices is A326619/A326620.

%Y The average of the set of distinct prime factors is A323171/A323172.

%Y Cf. A001221, A067629, A078174, A078175, A112798, A316413, A326621.

%K nonn,frac

%O 2,2

%A _Gus Wiseman_, Jul 14 2019