[seqfan] Re: Primary pretenders

[Tomasz Ordowski]

P.S. The smallest counterexample is a(10103) = 645 = 3*5*43.

pt., 17 sie 2018 o 06:53 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Dear SeqFans!
>
> All distinct terms of the primary pretenders are
>
> https://oeis.org/A108574
>
> These numbers k < 561 are semiprimes k = pq such that p-1 | q-1, where
> primes p <= q.
>
> Cf. Seidov's comment and https://oeis.org/A121707
>
> =========
>
> Let a(n) be the smallest composite k not being a Carmichael number such
> that n^k == n (mod k).
>
> The sequence is unbounded. Yes?
>
> Conjecture: The terms a(n) are all semiprimes k = pq such that p-1 | q-1,
> as above.
>
> Find the term a(10103) > 561. Cf. https://oeis.org/A000790
>
> The terms a(n) such that A000790(n) = 561.
>
> Best regards,
>
> Thomas
>
>
>
>