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

1,2

Links

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

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)

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 *)

Prog

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

Crossrefs

Cf. A136655, A126192.

Cf. A001227, A183063, A000593, A007955.

Sequence in context: A102208 A371650 A369779 * A009385 A008308 A176889

Adjacent sequences: A125908 A125909 A125910 * A125912 A125913 A125914

Keyword

nonn

Author

N. J. A. Sloane, Jul 14 2008

Status

approved