We give formulas expressing Milnor invariants of an n-component link L in the 3-sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant μ_L(J) vanishes for any sequence J with length at most k, then any Milnor μ-invariant μ_L(I) with length between 3 and 2k + 1 can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the "first nonvanishing" Milnor invariants can be always represented as such a linear combination.
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