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a(n) is the greatest common divisor of (n-1)! and n^n.
3

%I #14 Jun 29 2018 02:12:32

%S 1,1,1,2,1,24,1,16,9,640,1,20736,1,7168,6075,2048,1,23887872,1,

%T 8192000,321489,2883584,1,10319560704,625,54525952,59049,2877292544,1,

%U 835884417024000000,1,67108864,578739249,36507222016,187578125,61628086298345472,1

%N a(n) is the greatest common divisor of (n-1)! and n^n.

%C a(n) = 1 iff n is 1 or a prime.

%H Harry J. Smith, <a href="/A062763/b062763.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = A051696(n)/n.

%e a(10) = gcd(9!, 10^10) = gcd(2^7*3^4*5*7, 2^10*5^10) = 2^7*5 = 640.

%o (PARI) a(n)=gcd((n-1)!, n^n); \\ _Harry J. Smith_, Aug 10 2009

%Y Cf. A051696.

%K nonn

%O 1,4

%A _Henry Bottomley_, Jul 16 2001