[seqfan] The "lambda numbers" and a curiosity in PS

[Tomasz Ordowski]

Dear readers!

   Let lambda(n) denote the Carmichael function of n,
and let D_k be the denominator of Bernoulli number B_k.
Note that if p is a prime, then lambda(p) = lambda(D_{p-1}).
   Let's define:
Composites n such that lambda(n) = lambda(D_{n-1}).
   These are Carmichael numbers n such that
LCM_{prime p|n} (p-1) = LCM_{p-1|n-1 p prime} (p-1).
Carl Pomerance noted that Chernick's Carmichael number
n = 88189878776579929 may satisfy this strong condition.
This number is of the form (6k+1)(12k+1)(18k+1) for k = 40826.
   Amiram Eldar confirmed that it is the 54th term of the sequence
5615659951, 36901698733, 55723044637, 776733036121, 2752403727511, ...
He found 191 terms below 2^64 that I defined without believing they
existed.
Maybe someone will find an alternative definition of  these "lambda
numbers".
Together with Amiram, I will submit these numbers as a new OEIS sequence.

Best regards,

Thomas Ordowski
_____________
https://oeis.org/A002322
https://oeis.org/A027642
https://oeis.org/A317210
___________________________
P.S. On Carmichaels of the form D_{2m} / 2.

   Let D_k be the denominator of Bernoulli B_k as above.
For odd n > 1, we have D_{n-1} = Product_{p-1|n-1, p prime} p.
   Are there odd numbers n > 3 such that n - 1 | D_{n-1} / 2 - 1 ?
If so, then such D_{n-1} / 2 is a Carmichael number (divisible by 3),
   because lambda(D_{n-1}) = lambda(D_{n-1} / 2) | n - 1.
If not, let's try a weaker condition: lambda(D_{n-1}) | D_{n-1} / 2 - 1 >
2.
   Are there Carmichael numbers of the form D_{2m} / 2 ?
How to prove that such numbers do not exist?
_____________
https://oeis.org/A090126
https://oeis.org/history/view?seq=A248614&v=42
___________
The curiosity.
Numbers n such that n|D_n
in an interesting finite sequence:
1|2, 2|6, 6|42, 42|1806, and 1806|1806.
Cf. https://oeis.org/A014117 (see the third comment)
and https://www.bernoulli.org/~bk/denombneqn.pdf