[seqfan] Counting k! == +-1 (mod n), k>=0

[Richard J. Mathar]

i) Just by curiosity: is there anything known about the function w(n)
counting the number of k>=0 (or k>0 alternatively) such that k! = +-1 (mod n)?
This is mentioned in A071710. The interest would be in general n, prime or not.

Can we say, at least, that these k with that modular property are finite
for each n such that w(n) < infinity, although the candidates k are not
bounded by the definition?

ii) Is there a proper definition of the function "t" used in the multiplicative
formula in A058067 ? The problem in my eyes is that a(p^e) is not just a
power of p for e>1.

Richard Mathar