If I understand the problem correctly, then

my @dispersal;
my $maxpow = int(log($cash)/log(2) - 1);
@dispersal = map(2**$_, 0..$maxpow);
$dispersal[$#dispersal+1] = $cash - 2**($maxpow +1)+1;

my @envelope = sort { $a <=> $b } @dispersal;
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should correctly generate @envelope, although there is no need for @dispersal anymore.