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A039951
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Smallest prime p such that p^2 divides n^(p-1) - 1.
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14
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2, 1093, 11, 1093, 2, 66161, 5, 3, 2, 3, 71, 2693, 2, 29, 29131, 1093, 2, 5, 3, 281, 2, 13, 13, 5, 2, 3, 11, 3, 2, 7, 7, 5, 2, 46145917691, 3, 66161, 2, 17, 8039, 11, 2, 23, 5, 3, 2, 3
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OFFSET
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1,1
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COMMENTS
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a(n^k) <= a(n) for any n,k>1.
a(n) is currently unknown for n = {47, 72, 186, 187, 200, 203, 222, 231, 304, 311, 335, 347, 355, 435, 454, 542, 546, 554, 610, 639, 662, 760, 772, 798, 808, 812, 858, 860, 871, 983, 986, ...}.
a(47) > 3.4*10^13, a(72) > 2.1*10^13. (see Fischer's tables)
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LINKS
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Table of n, a(n) for n=1..46.
C. K. Caldwell, The Prime Glossary, Fermat quotient.
W. Keller and J. Richstein, Fermat quotients q_p(a) that are divisible by p.
Richard Fischer, Fermat quotients B^(P-1) == 1 (mod P^2)
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FORMULA
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a(4k+1) = 2.
a(n) = A096082(n) for all n > 1 that are not of the form 4k+1. (Note that A096082 begins with n = 2.)
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CROSSREFS
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Cf. A001220, A045616, A096082, A001220, A014127, A123692, A123693.
Sequence in context: A159858 A108963 A152510 * A135618 A119554 A036104
Adjacent sequences: A039948 A039949 A039950 * A039952 A039953 A039954
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KEYWORD
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nonn,more,hard
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AUTHOR
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David W. Wilson
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EXTENSIONS
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a(34)-a(46) from Helmut Richter (richter(AT)lrz.de), May 17 2004.
Entry revised by N. J. A. Sloane, Nov 30 2006
Edited by Max Alekseyev, Oct 06, Oct 09 2009
Second formula corrected and explained by Jonathan Sondow, Jun 17-18 2010
Edited and updated by Max Alekseyev, Jan 29 2012
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STATUS
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approved
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