A306451 - OEIS

%I #16 Mar 16 2019 13:17:29

%S 3,6,66,561,726,7107,8205,8646,62745,100101,140097,166521,237381,

%T 237945,566805,656601,876129,1053426,1095186,1194285,1234806,1590513,

%U 1598871,1938021,2381259,2518041,3426081,4125441,5398401,5454681,5489121,5720331,5961441

%N Non-coprime pseudoprimes or primes to base 3: numbers k that are multiples of 3 and are such that k divides 3^k - 3.

%C Union of {3} and (A122780 - {1} - A005935).

%C Numbers of the form 3*m such that 3^(3*m-1) == 1 (mod m).

%C The squarefree terms are listed in A306450.

%H Jianing Song, <a href="/A306451/b306451.txt">Table of n, a(n) for n = 1..163</a> (all terms below 10^9)

%F 66 is a term because 66 divides 3^66 - 3 = 3*(3^65 - 1) = 3*(3^5 - 1)*(3^60 + 3^55 + ... + 3^5 + 1) and 66 is divisible by 3.

%o (PARI) forstep(n=3, 1e7, 3, if(Mod(3, n)^n==3, print1(n, ", ")))

%Y Cf. A005935, A006935, A122780, A306450.

%Y A258801 is a subsequence.

%K nonn

%O 1,1

%A _Jianing Song_, Feb 17 2019