[seqfan] A proper subset of the phi-radical numbers

[Tomasz Ordowski]

Dear SeqFans!

   Conjecture:
The composite numbers n for which Od(lambda(n)) = Od(n-1)
are only Carmichael numbers n such that (n-1) / lambda(n) = 2^k for some k,
namely 7816642561, 49413980161, 32713826587115521, ... for k = 13, 13, 14,
...
   Cf. https://oeis.org/A174590

   Note that the above numbers are a proper subset of {A306478}.
See https://oeis.org/history/view?seq=A306478&v=21

   Hypothesis:
There are no composite numbers n such that Od(phi(n)) = Od(n-1).

We ask for counterexamples.

Best regards,

Ami Eldar & Tom Ordowski
______________________
Od(m) is the odd part of m:
 https://oeis.org/A000265