[seqfan] Absolute Euler pseudoprimes

[Tomasz Ordowski]

Applies to A033181 - OEIS.

It seems that all absolute Euler pseudoprimes n satisfy the stronger
congruence:
b^((n-1)/2) == 1 (mod n) for every base b coprime to n.  Could this be
true?
In their well-known definition, is a weaker condition: b^((n-1)/2) == +-1
(mod n).
Note that these pseudoprimes meet the modified Korselt's criterion, namely:
squarefree n is such a number iff p-1 divides (n-1)/2 for each prime
divisor p of n,
thus these are odd numbers n such that lambda(n) divides (n-1)/2.  Right?

Cf. https://oeis.org/history/view?seq=A033181&v=73 (see the last comment).

I am asking for comments.

Best regards,

Thomas Ordowski
____________________________
https://arxiv.org/pdf/1109.3596.pdf
https://www.emis.de/journals/INTEGERS/papers/a7self/a7self.pdf
These special Carmichael numbers are the absolute Euler pseudoprimes, I
think.