A240098 Product of the greatest common divisors of n and k! over k=0..n-1.

1, 1, 1, 4, 1, 432, 1, 16384, 19683, 800000, 1, 5159780352, 1, 3373232128, 5189853515625, 281474976710656, 1, 499751156776108032, 1, 524288000000000000000, 262757514534242203161, 299170970322599936, 1, 48239864614087244084529856512, 2910383045673370361328125

Offset: 1

Author

R. J. Mathar, Apr 01 2014

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..395

Crossrefs

Cf. A058067.

Programs

Maple

A240098 := proc(n)
    mul( igcd(n,k!),k=0..n-1) ;
end proc:

Mathematica

Table[Times@@Table[GCD[i,n!],{n,0,i-1}],{i,30}] (* Harvey P. Dale, Feb 23 2015 *)

PARI

a(n) = vecprod(vector(n,k, gcd(n, (k-1)!))); \\ Michel Marcus, Sep 29 2020

Formula

a(n) = Product_{k=0..n-1} gcd(n,k!) = n^n/A058067(n).

a(p) = 1 for primes p. - Joerg Arndt, Apr 01 2014

a(p^2)= p^(p*(2*p-3)) for primes p. - R. J. Mathar, Apr 02 2014

Extensions

More terms from Harvey P. Dale, Feb 23 2015

a(20) corrected by Amiram Eldar, Sep 29 2020