Unitary hyperperfect numbers

On Modified Hyperperfect Numbers

We introduce the so-called modified hyperperfect numbers, and completely determine their form in the case of classical divisors, unitary, biunitary, and e-divisors, respectively. AMS Subject classification (2000): 11A25.

Unitary untouchable numbers

In 1973, Erdős proved that a positive proportion of numbers are untouchable; that is, not of the form s(n), where s(n) := σ(n)−n is the sum of the proper divisors of n. We investigate the analogous question where σ is replaced with similar divisor functions, such as the unitary sum-of-divisors function σ∗ (which sums those divisors d of n co-prime to n/d). We use the slightly modified version o...

2 9 Fe b 20 08 Unitary super perfect numbers ∗ †

We shall show that 9, 165 are all of the odd unitary super perfect numbers.

Polynomial Identities for Orbit Numbers of General Linear and Unitary Groups over Finite Fields

On Elementary Unitary and Φ-unitary Transformations

We introduce a simple uniform structure of elementary Φ-unitary matrices. Elementary Φ-unitary transformations are the extentions of Householder transformations in real and complex spaces with a definite or an indefinite inner product induced by a nonsingular signature matrix Φ. The extentions are found useful in the computations of complex matrices or special structured matrices. For two (comp...