On the problem of odd h-fold perfect numbers

M. Artuhov

Displaying similar documents to “On the problem of odd h-fold perfect numbers”

Note on perfect and multiply perfect numbers

McCarthy, Paul J. (1957)

Portugaliae mathematica

Similarity:

Odd perfect numbers

Jan Slowak (1999)

Mathematica Slovaca

Similarity:

Sylvester: ushering in the modern era of research on odd perfect numbers.

Gimbel, Steven, Jaroma, John H. (2003)

Integers

Similarity:

An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers.

McDaniel, Wayne L. (1990)

International Journal of Mathematics and Mathematical Sciences

Similarity:

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.

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.