A071248 a(n) = Product_{k=1..n} lcm(n,k).

1, 4, 54, 768, 75000, 466560, 592950960, 5284823040, 1735643790720, 45360000000000, 1035338990313196800, 102980960177356800, 145077660657859734604800, 154452450072526199193600

Offset: 1

Author

Amarnath Murthy, May 21 2002

Keywords

• nonn

Comments

Log(a(n))/n/Log(n) is bounded since n^n < a(n) < n^(2n). It seems that lim n -> infinity Log(a(n))/n/Log(n) exists and = 1.7.... - Benoit Cloitre, Aug 13 2002

Links

• T. D. Noe, Table of n, a(n) for n=1..100

Crossrefs

Product of terms in n-th row of A051173.

Cf. A067911, A056916, A055774.

Programs

Maple

A071248 := proc(n) mul( lcm(k,n),k=1..n) ; end: for n from 1 to 10 do printf("%d ",A071248(n)) ; od ; # R. J. Mathar, Apr 03 2007

Mathematica

Table[Product[LCM[k,n],{k,n}],{n,20}] (* Harvey P. Dale, Jun 12 2019 *)

PARI

a(n)=prod(k=1,n,lcm(n,k))

Formula

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

a(n) = n!*n^n/A067911(n)=A000142(n)*A000312(n)/A067911(n). - R. J. Mathar, Apr 03 2007

Extensions

More terms from Benoit Cloitre, Aug 13 2002