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

1,4

Links

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

Formula

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

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

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 *)

Prog

(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

Crossrefs

Cf. A001222, A007947, A205959, A008578.

Sequence in context: A226604 A154213 A353920 * A176456 A351211 A033812

Adjacent sequences: A363920 A363921 A363922 * A363924 A363925 A363926

Keyword

nonn

Author

Peter Luschny, Jul 11 2023

Status

approved