As much as I understood, you don't actually need to login to see the needed pages. Otherwise, this seems to do what you want to do (or something resembling it):

use strict;
use warnings;
use Fatal qw/ open close /;
use WWW::Mechanize;
use Carp;
     
my $mech =  WWW::Mechanize->new( autocheck => 1 );  

open my $pro_list, '>>', 'profiles.out';
for my $curr_page (1..3) {
        $mech->get("http://indiecharts.com/indie_Music_Artists.asp?Key
+word=&Page=$curr_page&butname=");
        my @artist_links = $mech->find_all_links(url_regex => qr/\d{9}
+/);
        print scalar @artist_links, " matching links on page $curr_pag
+e\n";
        for my $artist_link (@artist_links) {
                print $pro_list $artist_link->text(), "\n";
        }
}
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