[seqfan] Re: Looking for help with a formula

[William Keith]

On Aug 28, 2009, at 2:05 PM, David Wilson wrote:

> I have a PDF of an old journal article that gives a formula for the
> number of distinct residues of nth powers mod m (which the article call
> w_k(m)). The wording of the formula is somewhat arcane.
>
> I have tried to implement this formula, but I have not been able to
> identify the Lucas function referenced in the formula (the Euler
> function is the totient). The analysis is aggravated by the fact that
> this Lucas function is evaluated only at powers of 2 in the formula.
>
> If anyone would like to lend me a hand with this, I would be very
> appreciative, since I have wanted to extend some residue-counting
> sequences (A000993 et al).

Sounds interesting; maybe I could help simplify.  What's the article 
ref, or send the pdf this way?

William Keith