A069141 - OEIS

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

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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