Correcting a few typos in BrowserUk otherwise excellent post:

use Math::BaseCalc;

my $bc = Math::BaseCalc->new( 
    digits=> [ 'A' .. 'Z', 'a' .. 'z', 2 .. 9 ]
);
print $bc->to_base( 99999999 );

print $bc->from_base( 'Hq7un' );
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If you want to distribute the maping from 10^8 => 60^8 in some non-guessable fashion, you've a some more work to do.

From the "obfu" in the title, I get the sense that this is what the OP intended; some type of bit shuffling may be sufficient to ensure that the sequence is not predictable, but I'm not sure how best to go about it...