%I A115092
%S A115092 1,1,1,2,2,1,1,2,3,2,1,1,1,2,2,1,4,4,3,7,1,4,4,1,1,1,3,1,2,1,2,2,4,2,2,
%T A115092 1,1,2,1,1,2,1,2,2,1,2,1,1,5,1,2,2,1,3,3,2,3,3,2,1,1,5,4,2,1,3,1,1,2,1,
%U A115092 1,2,2,1,3,4,3,4,6,1,3,1,3,1,1,2,2,1,2,3,3,4,1,2,2,4,1,3,2,1,1,2,4,3,4
%N A115092 The number of m such that prime(n) divides m!+1.
%C A115092 By Wilson's theorem, we know that for each prime p there is at least 
               one m such that p divides m!+1. The largest such m is p-1. Sequence 
               A073944 lists the smallest m for each prime.
%H A115092 T. D. Noe, <a href="b115092.txt">Table of n, a(n) for n=1..2000</a>
%e A115092 a(20)=7 because 71, the 20th prime, divides m!+1 for the seven values 
               m=7,9,19,51,61,63,70. Interesting, note that 7+63=9+61=19+51=70.
%t A115092 Table[p=Prime[i]; cnt=0; f=1; Do[f=Mod[f*m,p]; If[f+1==p,cnt++ ], {m,
               p-1}]; cnt, {i,150}]
%Y A115092 Sequence in context: A098281 A103343 A085263 this_sequence A011847 A091325 
               A143974
%Y A115092 Adjacent sequences: A115089 A115090 A115091 this_sequence A115093 A115094 
               A115095
%K A115092 nonn
%O A115092 1,4
%A A115092 T. D. Noe (noe(AT)sspectra.com), Mar 01 2006