$seq is a scalar that has been assigned the value of an empty string.

Your code is attempting to access $seq as an object.

I think what you need to do is to use the object $seqio instead, so your code should read:

$hash{ $seqio->accession_number() }= $seqio->seq();
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Also - it would be helpful to indicate what error you are getting. "I'm having a problem" is rather imprecise.