Search: id:A039951
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%I A039951
%S A039951 2,1093,11,1093,2,66161,5,3,2,3,71,2693,2,29,29131,1093,2,5,3,281,2,13,
%T A039951 13,5,2,3,11,3,2,7,7,5,2,46145917691,3,66161,2,17,8039,11,2,23,5,3,2,3
%N A039951 Smallest prime p such that p^2 divides n^(p-1) - 1.
%C A039951 a(n^k) <= a(n) for any n,k>1.
%C A039951 a(n) is currently unknown for n = {47,72,139,160,186,187,200,203,222,
               231,304,311,335,347,355,387,435,454,464,542,546,552,554,594,610,639,
               648,662,666,715,758,560,772,798,804,808,612,858,860,871,886,983,986,
               ...}.
%C A039951 a(47) > 5.11*10^11 (see Richter's table).
%H A039951 C. K. Caldwell, The Prime Glossary, <a href="http://primes.utm.edu/glossary/
               page.php?sort=FermatQuotient">Fermat quotient</a>.
%H A039951 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 A039951 Helmut Richter, <a href="http://www.lrz-muenchen.de/~hr/tmp/A039951.txt">
               Table of all known a(n) up to n = 1000</a> (second column)
%F A039951 a(4k+1) = 2.
%F A039951 a(n) = A096082(n) for all n that are not of the form 4k+1.
%Y A039951 Cf. A001220, A045616, A096082, A001220, A014127, A123692, A123693.
%Y A039951 Sequence in context: A108963 A152510 A013543 this_sequence A135618 A119554 
               A036104
%Y A039951 Adjacent sequences: A039948 A039949 A039950 this_sequence A039952 A039953 
               A039954
%K A039951 nonn,more,hard
%O A039951 1,1
%A A039951 David W. Wilson (davidwwilson(AT)comcast.net)
%E A039951 a(34)-a(46) from Helmut Richter (richter(AT)lrz.de), May 17 2004.
%E A039951 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Nov 30 2006
%E A039951 Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 06 2009
%E A039951 Further edited by Max Alekseyev (maxale(AT)gmail.com), Oct 09 2009

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