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A102457 Least k >= 2 with n^(kn) == n (mod kn), also n^(kn-1) == 1 (mod k). 5
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; text; internal format)
OFFSET
2,1
COMMENTS
Motivated by even base-2 pseudoprime 161038, I inquired 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) [W. Edwin Clark] and is satisfied 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.
LINKS
MATHEMATICA
Array[Block[{k = 2}, While[PowerMod[#, k # - 1, k] != 1, k++]; k] &, 93, 2] (* Michael De Vlieger, Nov 13 2018 *)
PROG
(PARI) A102457(n) = { for(k=2, oo, if(1==(Mod(n, k)^((k*n)-1)), return(k)); ); } \\ Antti Karttunen, Nov 10 2018
CROSSREFS
Cf. A092067. - R. J. Mathar, Aug 30 2008
Sequence in context: A251377 A204051 A218248 * A102459 A347906 A329188
KEYWORD
nonn
AUTHOR
David W. Wilson, Jan 09 2005
STATUS
approved

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Last modified June 15 22:50 EDT 2024. Contains 373412 sequences. (Running on oeis4.)