A062758 Product of squares of divisors of n.

1, 4, 9, 64, 25, 1296, 49, 4096, 729, 10000, 121, 2985984, 169, 38416, 50625, 1048576, 289, 34012224, 361, 64000000, 194481, 234256, 529, 110075314176, 15625, 456976, 531441, 481890304, 841, 656100000000, 961, 1073741824, 1185921

Offset: 1

Author

Labos Elemer, Jul 16 2001

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A000005, A007955.

Programs

Mathematica

Times@@(Divisors[#]^2)&/@Range[40] (* Harvey P. Dale, Jan 14 2011 *)
a[n_] := n^DivisorSigma[0, n]; Array[a, 40] (* Amiram Eldar, Jun 11 2022 *)

PARI

a(n) = { n^numdiv(n) } \\ Harry J. Smith, Aug 10 2009

Formula

a(n) = n^tau(n) = n^A000005(n) = A007955(n)^2.

A007318(n,k) <= a(n). - Reinhard Zumkeller, Mar 04 2008