%------------------------------------------------------------------------
%
% Matlab script to factor the integers from 1 to n, and then
% count how many factors each integer has. This counts repetitions,
% so 12 = 2*2*3 counts as three factors. Results are plotted.
%
% Features intended to be shown here:
%
%   > how to format numbers when you don't know how many there are,
%
%   > custom of saving all plots to image files and all of the
%       computed data to a Matlab binary file,
%
%   > using the hist() function
%
%------------------------------------------------------------------------
%
%    Randall Bramley
%    Department of Computer Science
%    Indiana University, Bloomington
%    bramley somewhere around cs dot indiana dot (allegedly) edu
%
%    Initiated    : Mon 09 Mar 2009,  8:44 PM
%    Last Modified: Mon 09 Mar 2009, 12:46 PM to add these comments
%
%------------------------------------------------------------------------

n   = 100000;
f   = zeros(n, 1);
fid = fopen('factors', 'w');
for i = 1:n
    fI = factor(i);
    f(i) = length(fI);
    fprintf(fid, '%d:\t', i); 
    %-------------------------------------------------------------------
    % Here is the trick for handling unknown number of values to print.
    % Matlab will cycle through the format specifier over and over until
    % it has printed all of the values in fI.
    %-------------------------------------------------------------------
    fprintf(fid, '%d\t', fI); 
    fprintf(fid, '\n');
end
fclose(fid);

figure;
plot(1:n, f, 'b+')
title('Number of prime factors of integers 1:n')
xlabel('Integer')
ylabel('Number of Factors')
print -dpng Factors.png

s     = unique(f);
fn    = length(s);
nbars = max(10, fn);

disp(sprintf('Maximum number of prime factors: %d', max(s)));
disp(sprintf('Length of vector of unique numbers of prime factors: %d', fn));

figure;
hist(f, nbars)
title('Number of prime factors of integers 1:n')
xlabel('Number of Factors')
ylabel('Number of Integers with Given Number of Factors')
print -dpng histygram.png

save factor_info