A363923 a(n) = n^npf(n) / rad(n), where npf(n) is the number of prime factors with multiplicity of n.

1, 1, 1, 8, 1, 6, 1, 256, 27, 10, 1, 288, 1, 14, 15, 32768, 1, 972, 1, 800, 21, 22, 1, 55296, 125, 26, 6561, 1568, 1, 900, 1, 16777216, 33, 34, 35, 279936, 1, 38, 39, 256000, 1, 1764, 1, 3872, 6075, 46, 1, 42467328, 343, 12500, 51, 5408, 1, 1417176, 55, 702464

Offset: 1

Author

Peter Luschny, Jul 11 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A007947, A205959, A008578.

Programs

Maple

with(NumberTheory): a := n -> n^NumberOfPrimeFactors(n) / Radical(n):
seq(a(n), n = 1..56);

Mathematica

Array[#^PrimeOmega[#]/(Times @@ FactorInteger[#][[All, 1]]) &, 56] (* Michael De Vlieger, Jul 11 2023 *)

PARI

a(n) = my(f=factor(n)); n^bigomega(f)/factorback(f[, 1]); \\ Michel Marcus, Jul 11 2023

Python

from math import prod
from sympy import factorint
def A363923(n): return prod(n**e//p for p, e in factorint(n).items()) # Chai Wah Wu, Jul 12 2023

Formula

a(n) = n^A001222(n) / A007947(n).

a(n) = 1 <=> n term of A008578.