[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).
http://mathworld.wolfram.com/GiugaNumber.html
https://en.wikipedia.org/wiki/Giuga_number
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?
____________________
https://oeis.org/A014117
More information about the SeqFan
mailing list