A145643 Cubefree part of n!!.

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

Chai Wah Wu, Table of n, a(n) for n = 1..500

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

Adjacent sequences: A145640 A145641 A145642 * A145644 A145645 A145646

Keyword

nonn

Author

Artur Jasinski, Oct 15 2008

Status

approved