A306451 Non-coprime pseudoprimes or primes to base 3: numbers k that are multiples of 3 and are such that k divides 3^k - 3.

3, 6, 66, 561, 726, 7107, 8205, 8646, 62745, 100101, 140097, 166521, 237381, 237945, 566805, 656601, 876129, 1053426, 1095186, 1194285, 1234806, 1590513, 1598871, 1938021, 2381259, 2518041, 3426081, 4125441, 5398401, 5454681, 5489121, 5720331, 5961441

Offset: 1

Author

Jianing Song, Feb 17 2019

Keywords

• nonn

Comments

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

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

The squarefree terms are listed in A306450.

Links

• Jianing Song, Table of n, a(n) for n = 1..163 (all terms below 10^9)

Crossrefs

Cf. A005935, A006935, A122780, A306450.

A258801 is a subsequence.

Programs

PARI

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

Formula

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.