  We define a primitive index of an integer in a sequence to be the index of
the term with the integer as a primitive divisor. For the sequences $k^u+h^u$
and $k^u-h^u$, we discern a formula to find the primitive indexes of any
composite number given the primitive indexes of its prime factors. We show how
this formula reduces to a formula relating the multiplicative order of $k$
modulo $N$ to that of its prime factors. We then introduce immediate
consequences of the formula: certain sequences which yield the same primitive
indexes for numbers with the same unique prime factors, an expansion of the
lifting the exponent lemma for $v_2(k^n+h^n)$, a simple formula to find any
Zsigmondy number, a note on a certain class of pseudoprimes titled
overpseudoprime, and a proof that numbers such as Wagstaff numbers are either
overpseudoprime or prime.
