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A303975
Number of distinct prime factors in the product of prime indices of n.
36
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).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 28 2018
STATUS
approved