%I A096082
%S A096082 1093,11,1093,20771,66161,5,3,11,3,71,2693,863,29,29131,1093,3,5,3,281
%N A096082 Smallest odd prime p such that p^2 | n^(p-1) - 1.
%C A096082 Similar to the sequence A039951 where p=2 is allowed.
%C A096082 a(n^k) <= a(n) for any n,k>1.
%C A096082 a(21) > 2.6925*10^11.
%H A096082 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php/FermatQuotient.html">Fermat quotient</a>
%H A096082 W. Keller and J. Richstein, <a href="http://www.informatik.uni-giessen.de/
               staff/richstein/cnth/FermatQuotient.html">Fermat quotients q_p(a) 
               that are divisible by p</a>
%H A096082 W. Keller and J. Richstein, <a href="http://www.informatik.uni-giessen.de/
               staff/richstein/cnth/gen_wief.dat">Solutions of a^{p-1} == 1 (mod 
               p^2) for all a <= 1000 and odd primes p < 10^10</a>
%H A096082 W. Keller and J. Richstein, <a href="http://www.mscs.dal.ca/~joerg/res/
               fq.html">Fermat quotients q_p(a) that are divisible by p</a>.
%H A096082 Helmut Richter, <a href="http://www.lrz-muenchen.de/~hr/tmp/A039951.txt">
               Table of all known a(n) up to n = 1000</a>
%F A096082 a(n) = A039951(n) for all n not of the form 4k+1, while A039951(4k+1) 
               = 2. - Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 03 2006
%t A096082 f[n_] := Block[{k = 2}, While[k < 5181800 && PowerMod[n, Prime[k] - 1, 
               Prime[k]^2] != 1, k++ ]; If[k == 5181800, 0, Prime[k]]]; Table[ f[n], 
               {n, 70}] (from Robert G. Wilson v Jul 23 2004)
%Y A096082 Cf. A007663, A001220, A039951, A124121, 124122.
%Y A096082 Sequence in context: A043864 A043873 A091673 this_sequence A138698 A023698 
               A038469
%Y A096082 Adjacent sequences: A096079 A096080 A096081 this_sequence A096083 A096084 
               A096085
%K A096082 nonn,more,hard
%O A096082 2,1
%A A096082 Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 22 2004
%E A096082 Definition corrected by Alexander Adamchuk, Nov 27 2006
%E A096082 Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 07 2009