[seqfan] Triangular pretenders

[Tomasz Ordowski]

Dear SeqFans!

Let a(n) be the smallest triangular number t > 3 such that n^t == n (mod
t).

6, 6, 561, 6, 6, 10, 6, 6, 10, 6, 6, 10, 6, 6, 15, 6, 6, 10, 6, 6, 10, 6,
6, 28, ...

Note that a(n) > 6 if and only if n == 2 (mod 3).

The sequence is bounded, namely a(n) <= 561.

Problem: Find all distinct terms of the sequence.

Is this sequence periodic like the primary pretenders?
Does it have the basic period shorter than 23# 277# ?

Cf. http://oeis.org/A000217 and http://oeis.org/A000790

Best regards,

Thomas
_____________
I found a simple characteristic of the set of all distinct primary
pretenders:
http://oeis.org/history/view?seq=A108574&v=29 (the last comment).
Unfortunately, this has not been published yet. Why?