P gedankenexperimental code. Today: one of my conjectures

This is about a special case of the general sequence

  Lambda_a'(T, n) := [T/a_n] - \sum_{i=1}^{n - 1} Lambda_a'([T/a_n], i)
  Lambda_a'(T, 0) := 0

where a is a sequence of positive integers and T and n are non-negative
integers and [x] denotes the integral part of x.

Now my conjecture states that for any integral T:

  Lambda_p'(T, pi([sqrt(T)])) <= 5

where p is the sequence of primes, pi() is the prime counting function and
sqrt() is, of course, the square root.

This conjecture originally provoked this project of unicomplex! Well, it
didn't *provoke* or *demand* it but it was what I came up with searching
for a general solution to those recursion formulas. (A naive implementation
of the Lambda_p' sequence took three weeks to compute for all T <= 20,000
which is really bad. IIRC, the recursion complexity was huge -- something
around 2^pi(sqrt(T)) -- but I don't want to talk about this sequence now as
I'll continue writing it up as a paper as soon as I find time (the one still
present on my github account is BS and... yeah, I may remove that right now
:-)))