Ok, in http://www.algebra.uni-linz.ac.at/~noebsi/pub/smallrings.ps I find Theorem 1. [Sho38] Every finite ring R can be uniquely (up to isomorphism) decomposed into a direct sum of rings of prime power order. I assume this is analogous to the decomposition therem for finite abelian groups, and would imply A027623 is multiplicative. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"