A056916 Product of the orders of the elements in a cyclic group with n elements.

1, 2, 9, 32, 625, 648, 117649, 131072, 4782969, 12500000, 25937424601, 214990848, 23298085122481, 1771684761728, 14416259765625, 562949953421312, 48661191875666868481, 11712917736940032, 104127350297911241532841, 5120000000000000000, 7788651757984142343081

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), Feb 10 2002

Keywords

• nonn
• nice

Links

• Amiram Eldar, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A057660.

Cf. A067911, A071248.

Programs

Maple

a:=n->mul(denom (k/n), k=1..n): seq(a(n), n=1..18); # Zerinvary Lajos, Apr 26 2008

Mathematica

Table[Product[n/GCD[n,i],{i,0,n-1}],{n,30}] (* Harvey P. Dale, Oct 24 2011 *)

Formula

a(n) = Product_{ d divides n } d^phi(d). - Vladeta Jovovic, Sep 10 2004

Extensions

Edited by Dean Hickerson, Mar 04 2002