A127553 a(n) = Product_{k=1..n} lcm(k,n)/gcd(k,n).

1, 2, 18, 96, 15000, 6480, 84707280, 41287680, 21427701120, 56700000000, 94121726392108800, 2483144294400, 11159820050604594969600, 24625709514114508800, 620634514500000000000, 359450793240158011392000

Offset: 1

Author

Leroy Quet, Apr 02 2007

Keywords

• nonn

Examples

			a(6) = lcm(1,6)/gcd(1,6) * lcm(2,6)/gcd(2,6) * lcm(3,6)/gcd(3,6) * lcm(4,6)/gcd(4,6) * lcm(5,6)/gcd(5,6) * lcm(6,6)/gcd(6,6) = 6/1 * 6/2 * 6/3 * 12/2 * 30/1 * 6/6 = 6480.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..238

Crossrefs

Cf. A056789.

Programs

Maple

A067911 := proc(n) mul( gcd(k,n),k=1..n) ; end: A071248 := proc(n) mul( lcm(k,n),k=1..n) ; end: A127553 := proc(n) A071248(n)/A067911(n) ; end: for n from 1 to 30 do printf("%d, ",A127553(n)) ; od ; # R. J. Mathar, Apr 03 2007
a:=n->product(ilcm(k,n)/igcd(k,n),k=1..n): seq(a(n),n=1..18); # Emeric Deutsch, Apr 13 2007

Mathematica

Table[Product[LCM[k,n]/GCD[k,n],{k,n}],{n,20}] (* Harvey P. Dale, Jun 10 2017 *)

Formula

a(n) = A071248(n)/A067911(n). - R. J. Mathar, Apr 03 2007

Extensions

More terms from R. J. Mathar, Apr 03 2007