Ok, I think this makes sense:

$dec_perms = (stat("filename"))[2] & 07777;
$oct_perm_str = sprintf "%o", $perms;
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You and the decimal value of file perms from stat against an octal number to get your decimal permissions. Then feed it to sprintf to get octal permissions.

But why "07777"? I'm sure there's a reason but it seems arbitrary (and perhaps they why is really moot...)