On GCD-morphic sequences

This note is a response to one of the problems posed by Kwa´sniewski in [1, 2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence F is at the point product of primary GCD-morphic sequences and any GCD-morphic sequence is encoded by natural number valued sequence satisfying condition (C1). The problem of general importance-for example in number theory was formulated in [1, 2] while investigating a new class of DAG's and their correspondent p.o. sets encoded uniquely by sequences with combinatorially interpretable properties.