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A092028 a(n) is the smallest m > 1 such that m divides n^m-1. 4


%S 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,

%T 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,

%U 2,5,2,67,2,3,2,71,2,73,2

%N a(n) is the smallest m > 1 such that m divides n^m-1.

%C Each prime factor of n-1 is a solution of the equation Mod[n^x-1,x]=0, so a(n) is not greater than smallest prime factor of n-1. Conjecture 1: All terms of this sequence are primes. Conjecture 2: a(n) is the smallest prime factor of n-1 or For n>2 A092028(n)=A020639(n-1).

%H Charles R Greathouse IV, <a href="/A092028/b092028.txt">Table of n, a(n) for n = 3..10000</a>

%F a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ];k)

%e a(8)=7 because 7 divides 8^7-1 and there doesn't exist an m such that 1<m<7 and m divides 8^m-1.

%t a[n_] := (For[k=2, Mod[n^k-1, k]>0, k++ ];k);Table[a[n], {n, 3, 75}]

%o (PARI) a(n)=if(n%2, return(2)); my(m=3); while(Mod(n,m)^m!=1, m+=2); m \\ _Charles R Greathouse IV_, May 29 2014

%Y Cf. A020639.

%K nonn

%O 3,1

%A _Farideh Firoozbakht_, Mar 26 2004

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Last modified January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)