Divisor summatory function is a function that is a sum over the divisor function. It can be visualized as the count of the number of lattice points fenced off by a hyperbolic surface in k dimensions. My visualization is of a different conic , one of a parabola. In fact my lattice points are not arranged in a square either, they are arranged in parabolic coordinates. My lattice point counting algorithm is simple enough though.(adsbygoogle = window.adsbygoogle || []).push({});

for k = 0 --> floor [sqrt n]

SUM (d(n)) = SUM ((2*floor[(n - k^2)/k]) + 1)

my visualization:

http://dl.dropbox.com/u/13155084/prime.png [Broken]

reference:

http://en.wikipedia.org/wiki/Divisor_summatory_function#Definition

related:

http://mathworld.wolfram.com/GausssCircleProblem.html

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# Finding Primes: A Divisor summatory function

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