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A240098 Product of the greatest common divisors of n and k! over k=0..n-1. 2

%I #23 Sep 29 2020 04:22:10

%S 1,1,1,4,1,432,1,16384,19683,800000,1,5159780352,1,3373232128,

%T 5189853515625,281474976710656,1,499751156776108032,1,

%U 524288000000000000000,262757514534242203161,299170970322599936,1,48239864614087244084529856512,2910383045673370361328125

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

%H Amiram Eldar, <a href="/A240098/b240098.txt">Table of n, a(n) for n = 1..395</a>

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

%F a(p) = 1 for primes p. - _Joerg Arndt_, Apr 01 2014

%F a(p^2)= p^(p*(2*p-3)) for primes p. - _R. J. Mathar_, Apr 02 2014

%p A240098 := proc(n)

%p mul( igcd(n,k!),k=0..n-1) ;

%p end proc:

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

%o (PARI) a(n) = vecprod(vector(n,k, gcd(n, (k-1)!))); \\ _Michel Marcus_, Sep 29 2020

%Y Cf. A058067.

%K nonn,easy

%O 1,4

%A _R. J. Mathar_, Apr 01 2014

%E More terms from _Harvey P. Dale_, Feb 23 2015

%E a(20) corrected by _Amiram Eldar_, Sep 29 2020

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)