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

1,4

Links

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

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

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 *)

Prog

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

Crossrefs

Cf. A058067.

Sequence in context: A300140 A347554 A298939 * A094337 A345313 A038019

Adjacent sequences: A240095 A240096 A240097 * A240099 A240100 A240101

Keyword

nonn,easy

Author

R. J. Mathar, Apr 01 2014

Extensions

More terms from Harvey P. Dale, Feb 23 2015

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

Status

approved