A326567 Numerator of the average of the multiset of prime indices of n.

1, 2, 1, 3, 3, 4, 1, 2, 2, 5, 4, 6, 5, 5, 1, 7, 5, 8, 5, 3, 3, 9, 5, 3, 7, 2, 2, 10, 2, 11, 1, 7, 4, 7, 3, 12, 9, 4, 3, 13, 7, 14, 7, 7, 5, 15, 6, 4, 7, 9, 8, 16, 7, 4, 7, 5, 11, 17, 7, 18, 6, 8, 1, 9, 8, 19, 3, 11, 8, 20, 7, 21, 13, 8, 10, 9, 3, 22, 7, 2, 7

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

Bruce Nye, Table of n, a(n) for n = 2..8500

Example

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

Mathematica

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

Prog

(PARI) a(n) = my(f=factor(n)); numerator(sum(i=1, #f~, primepi(f[i, 1])*f[i, 2])/bigomega(f)); \\ Bruce Nye, Jun 28 2026

Crossrefs

Cf. A001222, A001414, A056239, A067629, A112798, A123528/A123529, A289508, A289509, A290103, A316413, A326568.

Sequence in context: A245367 A304740 A326619 * A381437 A066328 A373956

Adjacent sequences: A326564 A326565 A326566 * A326568 A326569 A326570

Keyword

nonn,frac

Author

Gus Wiseman, Jul 13 2019

Status

approved