[seqfan] (b^k-1)/(b-1) == 1 (mod k)

[Tomasz Ordowski]

Dear SeqFan!

Let a(n) be the smallest composite k such that

         b^k == b (mod (b-1)k)

for all integer bases 2 <= b <= n = 2, 3, 4, 5, ...

Conjecture: for n > 2, a(n) is a Carmichael number. Yes?

Can also consider the congruence b^(k-1) == 1 (mod (b-1)k).

Maybe someone will be interested in these sequences.

Please give me some initial terms.

Best regards,

Thomas