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

1,2

Links

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

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A007955.

Sequence in context: A059479 A094083 A168251 * A217854 A369866 A028822

Adjacent sequences: A062755 A062756 A062757 * A062759 A062760 A062761

Keyword

nonn,changed

Author

Labos Elemer, Jul 16 2001

Status

approved