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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..395
Crossrefs
Cf. A058067.
Programs
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Maple
A240098 := proc(n) mul( igcd(n,k!),k=0..n-1) ; end proc:
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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