A326620 Denominator of the average of the set of distinct prime indices of n.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1

Offset

2,5

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..88.

Example

The distinct prime indices of 12 are {1,2}, with average 3/2, so a(12) = 2.
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[Denominator[Mean[PrimePi/@First/@FactorInteger[n]]], {n, 2, 100}]

Crossrefs

Positions of 1's are A326621.

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

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

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

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

Cf. A001221, A067629, A078174, A078175, A112798, A316413.

Sequence in context: A349410 A317240 A348444 * A353372 A305501 A184170

Adjacent sequences: A326617 A326618 A326619 * A326621 A326622 A326623

Keyword

nonn,frac

Author

Gus Wiseman, Jul 14 2019

Status

approved