Does anyone think that factoring will be shown to be "fractal" in nature, following the work of Ken Ono. Are there patterns in composite numbers, as yet unknown, that make factoring easier?
If I interpret your question correctly: no, they don't, because of the prime number theorem.
The amazing thing is d(n) can be computed recursively:
d(n) = d(n-1)+d(n-2)-d(n-5)-d(n-7)+d(n-12)+d(n-15)-...
except if you get d(0) on the right hand-side, you must put in the number n itself.
Well this is rather interesting and more than a bit related to the topic of this thread...In other words, all primes greater than 3 are constructible in the following manner: sqrt (24*(Generalized Pentagonal Number_n) + 1), a fact which might naturally lead one to ask: Is this in some manner related to the Dedekind eta function? Conversely, working backwards, then (p^2 - 1)/24 for p > 3, will always be a Generalized Pentagonal Number