#!/usr/bin/perl
use strict;        # strict and warnings are your friends. USE THEM ALWAYS!
use warnings;
# 923876

my $num;
input();           # you need not dump all your functions into subs
                   # and certainly not into chained subs, but using chained subs
                   # here makes it easier for me to point out a few things

=head 

print "\n Press any key to exit"; # Utterly unnecessary - 
                                  # your program will exit when it runs out of 
$key = <STDIN>;                   # instructions, absent code to specifically do 
                                  # otherwise ... such as sub quit_or_repeat:
#End of Program

=cut


sub input
{
    print "Enter an integer that is between 0 and 9: ";  # no newline so user can
    chomp ($num = <STDIN>);                              # enter data at prompt
     test_input();
}

sub test_input 
{
    if ( $num =~ /^[1-8]$/ ) {   # 1...8 are the numbers "between 0 and 9" 
                                 # as spec'ed by the prompt in OP's code
        main();
    } else {
        print "Only single-digit, positive integers, 1 - 8, are allowed\n";
        input();
    }
}

sub main 
{
    for(my $i=1; $i<=$num; $i++) {
        print "$i "; 
    }
    print "\n";
    quit_or_repeat();    # sub called here actually does something
                         # contrast w/ the original "$key = <STDIN>
                         #                           # End of Program" 
}

sub quit_or_repeat 
{
    my $key = '';
    print "\n Press 'q' to quit or any other key to continue: ";
    chomp ($key = <STDIN>);
    if ( lc($key) eq 'q' ) {   # either 'q' or "Q" quits
        exit;
    } else {
        input();               # go another round
    }
}