proof that the sum of the iterated totient function is always odd
Given a positive integer , it is always the case that
Accepting as proven that and for , it is clear that summing up the iterates of the totient function up to is summing up a series of even numbers in descending order and that this sum is therefore itself even. Then, when we add the iterate, the sum turns odd.
As a bonus, this proves that no even number can be a perfect totient number.
|Title||proof that the sum of the iterated totient function is always odd|
|Date of creation||2013-03-22 16:34:26|
|Last modified on||2013-03-22 16:34:26|
|Last modified by||PrimeFan (13766)|