A102457 - OEIS

A102457

Least k >= 2 with n^(kn) == n (mod kn), also n^(kn-1) == 1 (mod k).

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

Antti Karttunen, Table of n, a(n) for n = 2..12620

Antti Karttunen, Data supplement: n, a(n) computed for n = 2..100000

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. A102458, A102459.

Cf. A092067. - R. J. Mathar, Aug 30 2008

Sequence in context: A251377 A204051 A218248 * A102459 A347906 A329188

Adjacent sequences: A102454 A102455 A102456 * A102458 A102459 A102460

KEYWORD

nonn

AUTHOR

David W. Wilson, Jan 09 2005

STATUS

approved