Search: id:A102457
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%I A102457
%S A102457 80519,2,3,2,5,2,7,2,3,2,11,2,13,2,3,2,17,2,19,2,3,2,23,2,5,2,3,2,29,2,
%T A102457 31,2,3,2,5,2,37,2,3,2,41,2,43,2,3,2,47,2,7,2,3,2,53,2,5,2,3,2,59,2,61,
%U A102457 2,3,2,5,2,67,2,3,2,71,2,73,2,3,2,7,2,79,2,3,2,83,2,5,2,3,2,89,2,7,2,3
%N A102457 Least k >= 2 with n^(kn) == n (mod kn), also n^(kn-1) == 1 (mod k).
%C A102457 Motivated by even base-2 pseudoprime 161038, I enquired into base-n pseudoprimes 
               kn that are multiples of n, i.e. n^(kn) == n (mod kn). This is equivalent 
               to n^(kn-1) == 1 (mod k) [Edwin Clark] and is satified by any k dividing 
               n-1 [Michael Reid]. For n >= 3, this guarantees the existence of 
               a(n) with 2 <= a(n) = k <= lpf(n-1) (lpf = least prime factor). For 
               most n, a(n) = lpf(n-1), exceptional n and a(n) are noted in A102458 
               and A102459.
%Y A102457 Cf. A102458, A102459.
%Y A102457 Cf. A092067. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 
               2008]
%Y A102457 Sequence in context: A112785 A106775 A133379 this_sequence A102459 A095946 
               A050517
%Y A102457 Adjacent sequences: A102454 A102455 A102456 this_sequence A102458 A102459 
               A102460
%K A102457 nonn
%O A102457 2,1
%A A102457 David W. Wilson (davidwwilson(AT)comcast.net), Jan 09 2005

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