[seqfan] Re: Wieferich primes, anti-Carmichael pseudoprimes, and ?

[Tomasz Ordowski]

P.S. My question can be formulated directly:

Are there odd composite numbers n such that
2^n == 2 (mod n D_{n-1}) and gcd(n, D_{n-1}) > 1 ?


pon., 6 wrz 2021 o 09:09 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Hello SeqFans!
>
> Let's define:
> Odd numbers n > 1 such that 2^{n-1} == 1 (mod n D_{n-1} / 2),
> where D_k is the denominator of Bernoulli number B_k.
>
> Such prime numbers are Wieferich primes A001220.
> Are there such composite numbers that are not in A316907 ?
> A316907 (anti-Carmichael pseudoprimes) is a proper subset.
>
> For odd n > 1, D_{n-1} = Product_{p prime, p-1 | n-1} p.
> Note that 2^{n-1} == 1 (mod D_{n-1} / 2) for every odd n > 1.
>
> Best regards,
>
> Thomas
> _____________
> A001220 - OEIS <https://oeis.org/A001220>
> A316907 - OEIS <https://oeis.org/A316907>
>
>