  Let NSymm be the Hopf algebra of noncommutative symmetric functions over the
integers. In this paper a description is given of its Lie algebra of primitives
over the integers, Prim(NSymm), in terms of recursion formulas. For each of the
primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a
recursively given divided power series over it. This gives another proof of the
theorem that the algebra of quasi-symmetric functions is free over the
integers.
