A303975 - OEIS

%I #43 Jan 01 2019 07:10:44

%S 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,

%T 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,

%U 2,2,2,1,2,2,2,1,2,2,2,1,1,1,1,1,2,2,2

%N Number of distinct prime factors in the product of prime indices of n.

%C 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.

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

%F a(n) = A001221(A156061(n)). - _Michel Marcus_, Jan 01 2019

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

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

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

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

%K nonn

%O 1,13

%A _Gus Wiseman_, Dec 28 2018