

A102457


Least k >= 2 with n^(kn) == n (mod kn), also n^(kn1) == 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
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OFFSET

2,1


COMMENTS

Motivated by even base2 pseudoprime 161038, I inquired into basen pseudoprimes kn that are multiples of n, i.e., n^(kn) == n (mod kn). This is equivalent to n^(kn1) == 1 (mod k) [W. Edwin Clark] and is satisfied by any k dividing n1 [Michael Reid]. For n >= 3, this guarantees the existence of a(n) with 2 <= a(n) = k <= lpf(n1) (lpf = least prime factor). For most n, a(n) = lpf(n1), 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



KEYWORD

nonn


AUTHOR



STATUS

approved



