|Factorization||3 × 7|
|Divisors||1, 3, 7, 21|
Note that a necessary condition for n is that for any a coprime to n, a and n - a must satisfy the condition above, therefore at least one of a and n - a must only have factor 2 and 5.
Let denote the quantity of the numbers smaller than n that only have factor 2 and 5 and that are coprime to n, we instantly have .
We can easily see that for sufficiently large n, , but , as n goes to infinity, thus fails to hold for sufficiently large n.
In fact, For every n > 2, we have
so fails to hold when n > 273 (actually, when n > 33).
Just check a few numbers to see that '= 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 21.