[seqfan] The congruence 1^{n-1} + 2^{n-1} + ... + (n-1)^{n-1} == phi(n) (mod n)

[Tomasz Ordowski]

Dear SeqFans,

I have a question:

Are there numbers n > 2 such that
Sum_{k=1..n-1} k^{n-1} == phi(n) (mod n)
that are not odd prime powers?

https://oeis.org/A061345

Best regards,

Thomas Ordowski
________________________
Cf. https://oeis.org/A000961
See the penultimate comment.
How to prove this conjecture?