A330342 - OEIS

%I #32 Feb 23 2020 17:29:25

%S 0,1,2,3,4,1,6,3,2,1,10,3,12,1,2,7,16,5,18,3,2,1,22,3,4,1,8,3,28,1,30,

%T 7,2,1,10,5,36,1,2,3,40,5,42,3,8,1,46,7,6,9,2,3,52,17,14,7,2,1,58,3,

%U 60,1,2,15,4,5,66,3,2,9,70,5,72,1,14,3,16,5,78,7,26,1,82,5,4,1,2,7,88,5

%N a(n) is the smallest k such that b^(n-1) == b^k (mod n) for all integers b.

%C Note that (n-1) == a(n) (mod lambda(n)), where lambda(n) = A002322(n).

%C For n > 1, a(n) = lambda(n) if and only if n is a prime or a Carmichael number. For n <> 1 and 4, a(n) = n-1 if and only if n is a prime.

%C For n > 2, a(n) = 1 if and only if n is a squarefree 2-Knodel number.

%C For n > 3, a(n) = 2 if and only if n is a 3-Knodel number.

%F a(n) = A(n) if A(n) >= A051903(n) or a(n) = A002322(n) + A(n) otherwise, where A(n) = ((n-1) mod A002322(n)).

%t a[n_] := Module[{k = 0}, While[!AllTrue[Range[n], PowerMod[#, n - 1, n] == PowerMod[#, k, n] &], k++]; k]; Array[a, 100] (* _Amiram Eldar_, Dec 11 2019 *)

%Y Cf. A000040, A002997, A002322, A033553, A050990, A051903, A276976.

%K nonn

%O 1,3

%A _Thomas Ordowski_, Dec 11 2019

%E More terms from _Amiram Eldar_, Dec 11 2019