A095683 Number of prime power divisors of n. If n = product p_i^r_i then d = product {p_i^s_i, 2 <= s_i <= r_i, s_i is prime} is a prime power divisor of n.

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

Offset: 1

Author

Yasutoshi Kohmoto

Keywords

• nonn
• easy
• mult

Comments

The number of coreful divisors of n that are terms of A056166 (a divisor of n is coreful if it has the same set of distinct prime factors as n, cf. A307958). - Amiram Eldar, Oct 31 2023

Examples

			n=16: prime power divisors of 16 are {2^2, 2^3}, so a(16) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000720, A056166, A095691, A181819, A307958.

Programs

Mathematica

Array[Boole[# == 1] + Times @@ Map[PrimePi, FactorInteger[#][[All, -1]] ] &, 120] (* Michael De Vlieger, Jul 19 2017 *)

PARI

A095683(n) = { my(f = factor(n), m = 1); for (k=1, #f~, m *= primepi(f[k, 2]); ); m; } \\ Antti Karttunen, Jul 19 2017

Python

from sympy import factorint, primepi, prod
def a(n): return 1 if n==1 else prod(primepi(e) for e in factorint(n).values())
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jul 19 2017

Formula

Multiplicative with a(p^e) = A000720(e). - Vladeta Jovovic, Jul 06 2004

Extensions

More terms from Vladeta Jovovic, Jul 06 2004