A324848 Number of prime indices of n (counted with multiplicity) that divide n.

0, 1, 0, 2, 0, 2, 0, 3, 0, 1, 0, 3, 0, 1, 1, 4, 0, 3, 0, 2, 0, 1, 0, 4, 0, 1, 0, 3, 0, 3, 0, 5, 0, 1, 0, 4, 0, 1, 0, 3, 0, 2, 0, 2, 1, 1, 0, 5, 0, 1, 0, 2, 0, 4, 1, 4, 0, 1, 0, 4, 0, 1, 0, 6, 0, 2, 0, 2, 0, 1, 0, 5, 0, 1, 2, 2, 0, 3, 0, 4, 0, 1, 0, 4, 0, 1, 0

Offset: 1

Author

Gus Wiseman, Mar 18 2019

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.

Examples

			The prime indices of 6776 are {1,1,1,4,5,5}, four of which {1,1,1,4} divide 6776, so a(6776) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

The version for distinct prime indices is A324852.

Positions of zeros are A324846.

Positions of ones are A324856.

Cf. A003963, A056239, A112798, A120383, A323440, A324704, A324847, A324849, A324850, A324853.

Programs

Mathematica

Table[Total[Cases[If[n==1,{},FactorInteger[n]],{p_,k_}:>k/;Divisible[n,PrimePi[p]]]],{n,100}]