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

Author

Gus Wiseman, Dec 28 2018

Keywords

• nonn

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).

Examples

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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