A125911 Product of the even divisors of n.

1, 2, 1, 8, 1, 12, 1, 64, 1, 20, 1, 576, 1, 28, 1, 1024, 1, 216, 1, 1600, 1, 44, 1, 110592, 1, 52, 1, 3136, 1, 3600, 1, 32768, 1, 68, 1, 373248, 1, 76, 1, 512000, 1, 7056, 1, 7744, 1, 92, 1, 84934656, 1, 1000, 1, 10816, 1, 11664, 1, 1404928, 1, 116, 1, 207360000, 1, 124, 1

Offset: 1

Author

N. J. A. Sloane, Jul 14 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A136655, A126192.

Cf. A001227, A183063, A000593, A007955.

Programs

Mathematica

Table[Times@@Select[Divisors[n],EvenQ],{n,70}] (* Harvey P. Dale, Jul 06 2017 *)
a[n_] := Module[{e = IntegerExponent[n, 2], o, d}, o = n/2^e; d = DivisorSigma[0, o]; n^(d*(e+1)/2)/o^(d/2)]; Array[a, 100] (* Amiram Eldar, Jun 26 2022 *)

PARI

a(n) = my(d=divisors(n)); prod(k=1, #d, if (!(d[k]%2), d[k], 1)); \\ Michel Marcus, Jun 08 2020

Formula

a(n) = A007955(n) / A136655(n).

From Wesley Ivan Hurt, Jun 08 2020: (Start)

a(n) = Product_{d|n, d even} d.

If n is odd or an even squarefree number, then a(n) = floor((2*n)^(1 - ceiling(n/2) + floor(n/2)) * (d(n)/4)). (End)