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 A038203 #14 Aug 03 2016 11:42:40
%S A038203 1,2,3,3,4,3,5,4,5,5,6,4,10,6,5,5,12,5,12,5,6,7,17,4,8,11,8,7,19,5,21,
%T A038203 6,8,13,7,6,26,13,11,5,29,6,26,8,6,18,31,5,11,8,13,12,35,8,9,7,14,20,
%U A038203 37,5,41,22,7,8,13,8,42,14,18,7,39,6,44,27,8,15,11,11,49,6,9,30,55,7
%N A038203 Number of distinct values of factorials mod n.
%C A038203 Assuming k! mod n is uniformly distributed mod n up to k = A002034(n), the first k! == 0 (mod n). This gives a(n) ~= (1-(1-1/n)^k)*n, which empirically appears to be a good estimate. For prime p, A002034(p) = p, so we would expect a(p) ~= (1-(1-1/p)^p)*p ~= (1-1/e)*p = 0.63212 p for large primes p. - _David W. Wilson_, Aug 01 2016
%H A038203 David W. Wilson, <a href="/A038203/b038203.txt">Table of n, a(n) for n = 1..10000</a>
%e A038203 a(15)=5 since factorials are 1, 2, 6, 24, 120, etc. which mod 15 are 1, 2, 6, 9, 0, etc. and so there are 5 distinct values.
%t A038203 nn=90;With[{frls=Range[nn]!},Table[Length[Union[Mod[#,n]&/@frls]],{n,nn}]] (* _Harvey P. Dale_, Oct 05 2011 *)
%o A038203 (PARI) a(n)=my(t=1); #Set(vector(n,k,t=t*k%n)) \\ _Charles R Greathouse IV_, Aug 03 2016
%Y A038203 Cf. A038204, A062169.
%K A038203 nonn
%O A038203 1,2
%A A038203 _David W. Wilson_