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A102457
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Least k >= 2 with n^(kn) == n (mod kn), also n^(kn-1) == 1 (mod k).
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2
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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.
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CROSSREFS
| Cf. A102458, A102459.
Cf. A092067. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 30 2008]
Sequence in context: A106775 A133379 A204051 * A102459 A095946 A050517
Adjacent sequences: A102454 A102455 A102456 * A102458 A102459 A102460
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net), Jan 09 2005
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