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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A062758.

Sequence in context: A190424 A322484 A066332 * A158977 A165823 A263690

Adjacent sequences: A069138 A069139 A069140 * A069142 A069143 A069144

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 08 2002

Extensions

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

Status

approved