[seqfan] Carmichael numbers of the forms D_{2k}/2 and D_{2k}/6

[Tomasz Ordowski]

Dear readers!

Let D_k be the denominator of Bernoulli number B_k.

  Problem:
Are there numbers n > 3 such that D_{n-1} = 2n ?
  Equivalently, Product_{p prime, p-1|n-1} p = 2n.
If so, it must be a Carmichael number divisible by 3.
Amiram Eldar found nothing below 2^64
in https://oeis.org/A258801

  Carl Pomerance:
I don't know the answer to this, but here's a variation:
Are there Carmichael numbers n where D_{n-1} = 6n?
If so, are there infinitely many?
In a paper I'm working on with Sam Wagstaff, we show
there is a positive proportion of primes p with D_{p-1} = 6p.
[Note that these are Safe primes: https://oeis.org/A005385]

Generally, composites n such that D_{n-1} = 6n.
310049210890163447, 18220439770979212619, ...
Two Carmichael numbers found by Amiram
(of course, they cannot be divisible by 3).

Best regards,

Thomas
_____________
https://oeis.org/A002997
https://oeis.org/A027642