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

Author

Artur Jasinski, Oct 15 2008

Keywords

• nonn

Links

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

Crossrefs

Cf. A004709, A050985, A006882, A069705 (cubefree part of 2^n), A145642.

Programs

Mathematica

CubefreePart[n_Integer?Positive] := Times @@ Power @@@ ({#[[1]], Mod[ #[[2]], 3]} & /@ FactorInteger[n]); Table[CubefreePart[n!! ], {n, 1, 40}]

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

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

Formula

a(n) = A050985(A006882(n)). - Michel Marcus, May 11 2020