A303975 Number of distinct prime factors in the product of prime indices of n.

0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2

Offset

1,13

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.

First appearance of n is A062447(n - 1).

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A001221(A156061(n)). - Michel Marcus, Jan 01 2019

Example

9193 has prime indices {10, 66} with product 660, which has 4 distinct prime factors {2, 3, 5, 11}, so a(9193) = 4.

Mathematica

Table[PrimeNu[If[n==1, 1, Times@@PrimePi/@First/@FactorInteger[n]]], {n, 100}]

Prog

(PARI) a(n) = my(v = factor(n)[, 1]); omega(prod(i = 1, #v, primepi(v[i]))) \\ David A. Corneth, Dec 29 2018

Crossrefs

Cf. A000961, A001055, A001221, A002110, A003963, A056239, A112798, A156061, A302242, A302505, A320325.

Sequence in context: A368734 A120728 A092149 * A171099 A337253 A127173

Adjacent sequences: A303972 A303973 A303974 * A303976 A303977 A303978

Keyword

nonn

Author

Gus Wiseman, Dec 28 2018

Status

approved