A145643 - OEIS

%I #24 Sep 07 2024 08:54:06

%S 1,2,3,1,15,6,105,6,35,60,385,90,5005,1260,75075,315,1276275,210,

%T 24249225,525,509233725,11550,11712375675,34650,2342475135,900900,

%U 2342475135,3153150,67931778915,28028,2105885146365,14014,2573859623335

%N Cubefree part of n!!.

%H Chai Wah Wu, <a href="/A145643/b145643.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = A050985(A006882(n)). - _Michel Marcus_, May 11 2020

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

%o (Python)

%o from sympy import factorint, prod

%o def A145643(n):

%o     return 1 if n <= 1 else prod(p**(e % 3) for p, e in factorint(prod(range(n,0,-2))).items())

%o # _Chai Wah Wu_, Feb 04 2015

%o (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

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

%K nonn

%O 1,2

%A _Artur Jasinski_, Oct 15 2008