A Generalization of Euler's Totient Function
Keywords:
Euler's Totient Function, Generalized Euler's Totient FunctionAbstract
J. Freed-Brown, M. Holder, M. E. Orrison and M. Vrable introduced a new generalization of Euler's totient function, , defined to be the number of sequences
of elements in
such that if
is the subgroup of
generated by
, then
<
<
<
<
They also defined the function to be
where
is the largest integer such that
is nonzero. They gave the formulas for
and
where
and
are distinct primes and
,
and
are natural numbers. In this article, some more properties of
and
are investigated.
