Section 25.4 Connecting to the Primes
Subsection 25.4.1 Connecting to Moebius
Let's begin by defining a new function. Here is its graph.
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def J(x):
end = floor(log(x)/log(2))
out = 0
for j in [1..end]:
out += 1/j*prime_pi(x^(1/j))
return out
def _(end=[20,40..2000]):
L1 = [(n,J(n)) for n in [1..end]]
plot_step_function(L1).show()
Definition 25.4.2.
We define
Fact 25.4.3.
If
Remark 25.4.4.
If that last use of Moebius inversion looked a little sketchy, it does to me too, but I cannot find a single source where it's complained about that