[seqfan] A007850 & A014117

Tomasz Ordowski tomaszordowski at gmail.com
Mon May 20 20:24:57 CEST 2019

Hello SeqFans!

As is well known, a composite n is a Giuga number
if and only if Sum_{k=1..n-1} k^{phi(n)} == -1 (mod n).

I have a question: Can this phi(n) Euler's totient function
be replaced by the Carmichael lambda(n) function?

Best regards,

Thomas Ordowski
Cf. https://oeis.org/A007850 (see the last comment).

P.S. In opposition to the Giuga numbers, let's define:
Numbers n such that Sum_{k=1..n-1} k^{phi(n)} == 1 (mod n).
Also here, this phi(n) can be replaced by the lambda(n).
We only get five numbers, namely: 1, 2, 6, 42, 1806.
Cf. A014117. Are these for sure the same numbers?

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