OFFSET
1,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..500
Rafael Jakimczuk, On the h-th free part of the factorial, International Mathematical Forum, Vol. 12, No. 13 (2017), pp. 629-634.
Eric Weisstein's World of Mathematics, Cubefree Part.
FORMULA
From Amiram Eldar, Sep 01 2024: (Start)
log(a(n)) = log(3) * n + o(n) (Jakimczuk, 2017). (End)
MATHEMATICA
CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[n! ], {n, 1, 40}]
PROG
(Python)
from operator import mul
from functools import reduce
from sympy import factorint
import math
def A145642(n):
return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(math.factorial(n)).items()])
# Chai Wah Wu, Feb 04 2015
(PARI) a(n) = my(f=factor(n!)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 15 2008
STATUS
approved