A126192 Product of the even divisors of 2n.

2, 8, 12, 64, 20, 576, 28, 1024, 216, 1600, 44, 110592, 52, 3136, 3600, 32768, 68, 373248, 76, 512000, 7056, 7744, 92, 84934656, 1000, 10816, 11664, 1404928, 116, 207360000, 124, 2097152, 17424, 18496, 19600, 5159780352, 148, 23104, 24336, 655360000, 164

Offset: 1

Author

N. J. A. Sloane, Jul 14 2008

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A007955, A136655, A125911.

Programs

Maple

seq(mul(2*t,t=numtheory:-divisors(n)),n=1..100); # Robert Israel, Feb 01 2019

Mathematica

Table[Times@@Select[Divisors[2n],EvenQ],{n,50}] (* Harvey P. Dale, Jul 19 2011 *)
a[n_] := 2^(d = DivisorSigma[0, n]) * n^(d/2); Array[a, 100] (* Amiram Eldar, Jun 26 2022 *)

Formula

a(n) = 2^A000005(n) * A007955(n). - Robert Israel, Feb 01 2019