Column 3 of Marshall table, p. 443. A143093 is the analogous enumeration, column 2 of Marshall table, if we view the K-structures as graded rings with distinguished element.
REFERENCES
Ido Efrat, Valuations, orderings and Milnor K-theory, Mathematical Surveys and Monographs, vol. 124, American Mathematical Society, 2006.
Murray Marshall, Book Review: Valuations, orderings and Milnor K-theory, by Ido Efrat, Bulletin of the American Mathematical Society, Vol. 45 (July 2008) No. 3, pp. 439-444.