On near-perfect and deficient-perfect numbers

• Autorzy: Min Tang , Xiao-Zhi Ren , Meng Li
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A25: Arithmetic functions; related numbers; inversion formulas

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 2
• Strony: 221-226

Daty

wydano

2013

Twórcy

autor

Min Tang

• Department of Mathematics, Anhui Normal University, Wuhu 241003, China

autor

Xiao-Zhi Ren

• School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

autor

Meng Li

• Department of Mathematics, Anhui Normal University, Wuhu 241003, China

Identyfikatory

DOI

10.4064/cm133-2-8