The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A096082 Smallest odd prime p such that p^2 | n^(p-1) - 1. 9
 3, 1093, 11, 1093, 20771, 66161, 5, 3, 11, 3, 71, 2693, 863, 29, 29131, 1093, 3, 5, 3, 281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Similar to the sequence A039951 where p=2 is allowed. a(n^k) <= a(n) for any n,k>1. a(21) > 1.63*10^14 (see Fischer's link). For all nonnegative integers n and k, a(n^(n^k)) = a(n). (see puzzle 762 in the links). Also a(n) = 3 if and only if mod(n, 36) is in the set {1, 8, 10, 19, 26, 28, 35}. - Farideh Firoozbakht and Jahangeer Kholdi, Nov 01 2014 LINKS Table of n, a(n) for n=1..20. C. K. Caldwell, The Prime Glossary, Fermat quotient Richard Fischer, Fermat quotients B^(P-1) == 1 (mod P^2) W. Keller and J. Richstein, Fermat quotients q_p(a) that are divisible by p Carlos Rivera, Puzzle 762. Conjecture from Ribenboim's book, The Prime Puzzles and Problems Connection. FORMULA a(n) = A039951(n) for all n not of the form 4k+1, while a(4k+1) > A039951(4k+1) = 2. - Alexander Adamchuk, Dec 03 2006 MATHEMATICA 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}] (* Robert G. Wilson v, Jul 23 2004 *) PROG (PARI) for(n=2, 20, forprime(p=3, 1e9, if(Mod(n, p^2)^(p-1)==1, print1(p, ", "); next({2}))); print1("--, ")) \\ Felix Fröhlich, Jul 24 2014 CROSSREFS Cf. A007663, A001220, A039951, A124121, 124122. Sequence in context: A004803 A065604 A062612 * A274994 A178195 A199236 Adjacent sequences: A096079 A096080 A096081 * A096083 A096084 A096085 KEYWORD nonn,more,hard AUTHOR Lekraj Beedassy, Jul 22 2004 EXTENSIONS Definition corrected by Alexander Adamchuk, Nov 27 2006 Edited by Max Alekseyev, Oct 07 2009 Edited and updated by Max Alekseyev, Jan 29 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 14:06 EDT 2023. Contains 365502 sequences. (Running on oeis4.)