[seqfan] Looking for help with a formula

[David Wilson]

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).