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

[Tomasz Ordowski]

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>