[Jprogramming] Mobius function

[Roger Hui]

There are indeed more efficient computations;
the best so far is one that avoids factoring.
If mertens0 is the expression in the appended msg
and mertens2 is the one that avoids factoring, then
the time-space numbers are:

mertens0 1e6      6.68734  8.59231e7
mertens2 1e6      0.183586 1.20705e7

http://www.jsoftware.com/jwiki/Essays/Mertens_Function



----- Original Message -----
From: Roger Hui <rhui000 at shaw.ca>
Date: Monday, September 17, 2007 13:55
Subject: Re: [Jprogramming] Mobius function
To: Programming forum <programming at jsoftware.com>

> The Mertens function of n is the sum of Mobius k for k from 1 to n.
> There should be a more efficient computation of it than
> 
> +/ @: (mobius"0) @: >: @ i.
> 
> http://en.wikipedia.org/wiki/Mertens_function
> http://en.wikipedia.org/wiki/Mobius_function