A326568 Denominator of the average of the multiset of prime indices of n.

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 3, 1, 3, 3, 1, 1, 5, 1, 3, 2, 3, 1, 4, 1, 4, 1, 2, 1, 4, 1, 1, 3, 1, 2, 3, 1, 1, 2, 3, 1, 5, 1, 2, 3, 3, 2, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 2, 6, 1, 1, 1, 1, 1, 3, 1, 4, 1, 2, 1, 5

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

Antti Karttunen, Table of n, a(n) for n = 2..65537

Index entries for sequences related to prime indices in the factorization of n.

Example

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

Mathematica

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

Prog

(PARI) A326568(n) = { my(f=factor(n)); denominator(sum(i=1, #f~, f[i, 2]*primepi(f[i, 1]))/bigomega(n)); }; \\ Antti Karttunen, Jan 28 2025

Crossrefs

a(n) is a divisor of Omega(n) = A001222(n).

Positions of 1's are A316413.

Cf. A001414, A056239, A067629, A112798, A123528/A123529, A289508, A289509, A290103, A316428, A326567, A326620.

Sequence in context: A323163 A322318 A014649 * A279817 A309386 A253642

Adjacent sequences: A326565 A326566 A326567 * A326569 A326570 A326571

Keyword

nonn,frac

Author

Gus Wiseman, Jul 13 2019

Extensions

Starting offset corrected from 0 to 2 and data section extended to a(108) by Antti Karttunen, Jan 28 2025

Status

approved