Have you considered taking and ?
I want to show there exists 2 constants such that:
where ,
where is the largest number such that
I accomplished to show the following: (more or less trivial)
as n is prime
as (i.e a power of only one prime)
otherwise (i.e. n+1 has at least 2 prime-divisors)
I believe these are useful observations, but I'm more or less stuck here. I hope someone can give me a little push in the right direction here...
OK, so i'll remind you that is bounded the following way:
Here denotes the number of primes p, with . Recall that
Thus we have . This leads to the following:
This proves the claim.
I don't have to bother myself with the boundaries for . The proof for this is in my course-notes.