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

Offset: 2

Author

Gus Wiseman, Jul 14 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 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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537
• Index entries for sequences related to prime indices in the factorization of n.

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.

Programs

Mathematica

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

PARI

A326620(n) = if(1==n,0,denominator(vecsum(apply(primepi,factor(n)[,1]))/omega(n))); \\ Antti Karttunen, Jan 28 2025

Extensions

Data section extended to a(105) by Antti Karttunen, Jan 28 2025