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Search: id:A039951
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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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+0
8
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n^k) <= a(n) for any n,k>1.
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,...}.
a(47) > 5.11*10^11 (see Richter's table).
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LINKS
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C. K. Caldwell, The Prime Glossary, Fermat quotient.
W. Keller and J. Richstein, Fermat quotients q_p(a) that are divisible by p.
Helmut Richter, Table of all known a(n) up to n = 1000 (second column)
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FORMULA
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a(4k+1) = 2.
a(n) = A096082(n) for all n that are not of the form 4k+1.
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CROSSREFS
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Cf. A001220, A045616, A096082, A001220, A014127, A123692, A123693.
Sequence in context: A108963 A152510 A013543 this_sequence A135618 A119554 A036104
Adjacent sequences: A039948 A039949 A039950 this_sequence 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 (davidwwilson(AT)comcast.net)
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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 (njas(AT)research.att.com), Nov 30 2006
Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 06 2009
Further edited by Max Alekseyev (maxale(AT)gmail.com), Oct 09 2009
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