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A145643
Cubefree part of n!!.
2
1, 2, 3, 1, 15, 6, 105, 6, 35, 60, 385, 90, 5005, 1260, 75075, 315, 1276275, 210, 24249225, 525, 509233725, 11550, 11712375675, 34650, 2342475135, 900900, 2342475135, 3153150, 67931778915, 28028, 2105885146365, 14014, 2573859623335
OFFSET
1,2
LINKS
FORMULA
a(n) = A050985(A006882(n)). - Michel Marcus, May 11 2020
MATHEMATICA
CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[n!! ], {n, 1, 40}]
PROG
(Python)
from sympy import factorint, prod
def A145643(n):
return 1 if n <= 1 else prod(p**(e % 3) for p, e in factorint(prod(range(n, 0, -2))).items())
# Chai Wah Wu, Feb 04 2015
(PARI) a(n) = my(f = factor(prod(i = 0, (n-1)\2, n - 2*i))); prod(i = 1, #f~, f[i, 1]^(f[i, 2] % 3)); \\ Amiram Eldar, Sep 07 2024
CROSSREFS
Cf. A004709, A050985, A006882, A069705 (cubefree part of 2^n), A145642.
Sequence in context: A102583 A030780 A193683 * A338208 A323155 A145142
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 15 2008
STATUS
approved