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

1,8

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A127844 A017877 A295976 * A219481 A361430 A298826

Adjacent sequences: A095680 A095681 A095682 * A095684 A095685 A095686

Keyword

nonn,easy,mult

Author

Yasutoshi Kohmoto

Extensions

More terms from Vladeta Jovovic, Jul 06 2004

Status

approved