Hello all. I have something in which there must be a contradiction but I cannot find it.

So let

be the usual Euler phi/totient function, and let

be a finite group. Then we have

(1)

where

= the number of cyclic subgroups of order

and

= the number of elements of order

in

.

Then we also have the theorem

(2)

But I have a theorem in my notes

which states

. But by (1), this is equivalent to the statement

.

But doesn't this contradict (2) ? Unless

which cannot be true otherwise there would be no point looking at

. Can anyone help?