This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051696 #30 Jul 02 2025 16:01:58
%S A051696 1,2,3,8,5,144,7,128,81,6400,11,248832,13,100352,91125,32768,17,
%T A051696 429981696,19,163840000,6751269,63438848,23,247669456896,15625,
%U A051696 1417674752,1594323,80564191232,29,25076532510720000000,31,2147483648
%N A051696 Greatest common divisor of n! and n^n.
%C A051696 a(n) also equals the smallest positive integer such that lcm(a(1), a(2), a(3), ... a(n)) = n!, for every positive integer n. - _Leroy Quet_, Apr 28 2007
%H A051696 T. D. Noe, <a href="/A051696/b051696.txt">Table of n, a(n) for n = 1..500</a>
%F A051696 a(n) = Product_{p|n} p^(sum{k >= 1} floor(n/p^k)), where the product runs over the distinct primes p that divide n. - _Leroy Quet_, Apr 28 2007
%F A051696 a(n) = n*A062763(n). - _R. J. Mathar_, Mar 11 2017
%F A051696 a(n) = (numerator of B(n, 1/n))/n^(n - 1), where B(.,.) is the Euler beta function. - _Arkadiusz Wesolowski_, Nov 22 2017
%F A051696 a(p) = p for p prime. - _Peter Luschny_, Nov 29 2017
%e A051696 a(4) = 8 since 4! = 24 and 4^4 = 256 and gcd(24, 256) = 8.
%e A051696 lcm(a(1), a(2), a(3), a(4), a(5), a(6)) = lcm(1, 2, 3, 8, 5, 144) = 6! = 720. (See comment.)
%p A051696 seq(igcd(n!, n^n), n=1..32); # _Peter Luschny_, Nov 29 2017
%t A051696 Table[GCD[n!, n^n], {n, 40}] (* _Harvey P. Dale_, Oct 20 2011 *)
%t A051696 Table[Numerator@Beta[n, 1/n]/n^(n - 1), {n, 32}] (* _Arkadiusz Wesolowski_, Nov 22 2017 *)
%K A051696 nonn,easy,nice
%O A051696 1,2
%A A051696 _Leroy Quet_
%E A051696 More terms from _James Sellers_, Dec 08 1999