A069141 a(n) = n^2*(n+1)!/(n^tau(n)) where tau(n) is the number of divisors of n.

2, 6, 24, 30, 720, 140, 40320, 5670, 403200, 399168, 479001600, 300300, 87178291200, 6671808000, 92990177280, 86837751000, 6402373705728000, 1158789632000, 2432902008176640000, 319318388573184, 2548754484756480000, 53413257724968960000, 620448401733239439360000

Offset: 1

Author

Benoit Cloitre, Apr 08 2002

Keywords

• easy
• nonn

Comments

The expression n^2*(n+1)!/(n^tau(n)) is always an integer. n^tau(n) is also the product of square divisors of n (cf. A062758).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..448

Crossrefs

Cf. A000005, A062758.

Programs

Mathematica

a[n_] := (n+1)! / n^(DivisorSigma[0,n] - 2); Array[a, 23] (* Amiram Eldar, Aug 03 2024 *)

PARI

a(n) = (n+1)! / n^(numdiv(n)-2); \\ Amiram Eldar, Aug 03 2024

Extensions

a(22)-a(23) from Amiram Eldar, Aug 03 2024