Since you can sort on catalogue number, you can loop over the sorted keys and skip the ones not in the range:

foreach my $key (@sorted) {
    next unless $key eq '614' .. $key eq 'C18';
    print "$key: $db{$key} \n";
}
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Assuming the hash is %db. I suspect you were doing something similar but using the sort N field? The downfall is that you need to get the whole list of keys into memory --- with DB_File that could be avoided.