Displaying similar documents to “A basic approach to the perfect extensions of spaces”

On near-perfect and deficient-perfect numbers

Min Tang, Xiao-Zhi Ren, Meng Li (2013)

Colloquium Mathematicae

Similarity:

For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.

Linking the closure and orthogonality properties of perfect morphisms in a category

David Holgate (1998)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.

Odd perfect numbers of a special form

Tomohiro Yamada (2005)

Colloquium Mathematicae

Similarity:

We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.