A324852 Number of distinct prime indices of n that divide n.

0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1

Offset

1,6

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

Alois P. Heinz, Table of n, a(n) for n = 1..65536

Example

60060 has 7 prime indices {1,1,2,3,4,5,6}, all of which divide 60060, and 6 of which are distinct, so a(60060) = 6.

Maple

a:= n-> add(`if`(irem(n, numtheory[pi](i[1]))=0, 1, 0), i=ifactors(n)[2]):
seq(a(n), n=1..120);  # Alois P. Heinz, Mar 19 2019

Mathematica

Table[Count[If[n==1, {}, FactorInteger[n]], {p_, _}/; Divisible[n, PrimePi[p]]], {n, 100}]

Prog

(PARI) a(n) = {my(f = factor(n)[, 1]); sum(k=1, #f, !(n % primepi(f[k]))); } \\ Michel Marcus, Mar 19 2019

Crossrefs

The version for all prime indices (counted with multiplicity) is A324848.

Positions of zeros are A324846.

Positions of ones are A323440.

Cf. A000720, A001222, A003963, A056239, A120383.

Cf. A324704, A324771, A324847, A324849, A324850, A324853, A324856.

Sequence in context: A339813 A178111 A178112 * A363854 A353967 A035169

Adjacent sequences: A324849 A324850 A324851 * A324853 A324854 A324855

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved