Numbers whose positive divisors have small integral harmonic mean

A positive integer n is said to be harmonic when the harmonic mean H(n) of its positive divisors is an integer. Ore proved that every perfect number is harmonic. No nontrivial odd harmonic numbers are known. In this article, the list of all harmonic ...

A novel even-order harmonic mixer is proposed. Based on the translinear loop of BJT/HBTs, frequency doubling and single-to-differential conversion circuits have been employed in the design of harmonic mixer. The proposed mixer has been verified in a ...

In this paper, we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are rational and ...