A326619 - OEIS

A326619

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

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

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OFFSET

2,2

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.

LINKS

Table of n, a(n) for n=2..82.

EXAMPLE

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

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.

MATHEMATICA

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