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

%I A240098 #23 Sep 29 2020 04:22:10
%S A240098 1,1,1,4,1,432,1,16384,19683,800000,1,5159780352,1,3373232128,
%T A240098 5189853515625,281474976710656,1,499751156776108032,1,
%U A240098 524288000000000000000,262757514534242203161,299170970322599936,1,48239864614087244084529856512,2910383045673370361328125
%N A240098 Product of the greatest common divisors of n and k! over k=0..n-1.
%H A240098 Amiram Eldar, <a href="/A240098/b240098.txt">Table of n, a(n) for n = 1..395</a>
%F A240098 a(n) = Product_{k=0..n-1} gcd(n,k!) = n^n/A058067(n).
%F A240098 a(p) = 1 for primes p. - _Joerg Arndt_, Apr 01 2014
%F A240098 a(p^2)= p^(p*(2*p-3)) for primes p. - _R. J. Mathar_, Apr 02 2014
%p A240098 A240098 := proc(n)
%p A240098     mul( igcd(n,k!),k=0..n-1) ;
%p A240098 end proc:
%t A240098 Table[Times@@Table[GCD[i,n!],{n,0,i-1}],{i,30}] (* _Harvey P. Dale_, Feb 23 2015 *)
%o A240098 (PARI) a(n) = vecprod(vector(n,k, gcd(n, (k-1)!))); \\ _Michel Marcus_, Sep 29 2020
%Y A240098 Cf. A058067.
%K A240098 nonn,easy
%O A240098 1,4
%A A240098 _R. J. Mathar_, Apr 01 2014
%E A240098 More terms from _Harvey P. Dale_, Feb 23 2015
%E A240098 a(20) corrected by _Amiram Eldar_, Sep 29 2020