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Search: id:A096082
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| A096082 |
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Smallest odd prime p such that p^2 | n^(p-1) - 1. |
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+0
6
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| 1093, 11, 1093, 20771, 66161, 5, 3, 11, 3, 71, 2693, 863, 29, 29131, 1093, 3, 5, 3, 281
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Similar to the sequence A039951 where p=2 is allowed.
a(n^k) <= a(n) for any n,k>1.
a(21) > 2.6925*10^11.
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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
W. Keller and J. Richstein, Solutions of a^{p-1} == 1 (mod p^2) for all a <= 1000 and odd primes p < 10^10
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
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FORMULA
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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
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A007663, A001220, A039951, A124121, 124122.
Sequence in context: A043864 A043873 A091673 this_sequence A138698 A023698 A038469
Adjacent sequences: A096079 A096080 A096081 this_sequence A096083 A096084 A096085
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KEYWORD
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nonn,more,hard
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 22 2004
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EXTENSIONS
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Definition corrected by Alexander Adamchuk, Nov 27 2006
Edited by Max Alekseyev (maxale(AT)gmail.com), Oct 07 2009
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