Displaying similar documents to “On the distribution of some integers related to perfect and amicable numbers”

On near-perfect numbers

Min Tang, Xiaoyan Ma, Min Feng (2016)

Colloquium Mathematicae

Similarity:

For a positive integer n, let σ(n) denote the sum of the positive divisors of n. We call n a near-perfect number if σ(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3⁴·7²·11²·19².

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.

On a sum of divisors problem.

De Koninck, Jean-Marie, Ivić, Aleksandar (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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 consecutive integers divisible by the number of their divisors

Titu Andreescu, Florian Luca, M. Tip Phaovibul (2016)

Acta Arithmetica

Similarity:

We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.