Topic
Friendly number
About: Friendly number is a research topic. Over the lifetime, 66 publications have been published within this topic receiving 798 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1964
TL;DR: Theorem of Euler's Totient Function and Theorem 1.1.2.1 as discussed by the authors and the Theorem 2.3.1 of the Diophantine Analysis of Second and Higher Degrees.
Abstract: Divisibility and Indeterminate Equations of First Degree. Diophantine Analysis of Second and Higher Degrees. Prime Numbers. Number of Divisors and Their Sum. Congruences. Euler's Totient Function and the Theorem of Euler. Representation of Numbers by Decimals in a Given Scale. Continued Fractions. Legendre's Symbol and Jacobi's Symbol. Mersenne Numbers and Fermat Numbers. Representations of Natural Numbers as Sums of Non-Negative kth Powers. Some Problems of the Additive Theory of Numbers. Complex Integers. Bibliography. Index.
409 citations
TL;DR: The main purpose of as mentioned in this paper is to construct new families of special numbers with their generating functions, which are related to the many well-known numbers, such as Bernoulli numbers, the Fibonacci numbers, Lucas numbers, Stirling numbers of the second kind and the central factorial numbers.
Abstract: The main purpose of this paper is to construct new families of special numbers with their generating functions. These numbers are related to the many well-known numbers, which are the Bernoulli numbers, the Fibonacci numbers, the Lucas numbers, the Stirling numbers of the second kind and the central factorial numbers. Our other inspiration of this paper is related to the Golombek's problem \cite{golombek} \textquotedblleft Aufgabe 1088, El. Math. 49 (1994) 126-127\textquotedblright . Our first numbers are not only related to the Golombek's problem, but also computation of the negative order Euler numbers. We compute a few values of the numbers which are given by some tables. We give some applications in Probability and Statistics. That is, special values of mathematical expectation in the binomial distribution and the Bernstein polynomials give us the value of our numbers. Taking derivative of our generating functions, we give partial differential equations and also functional equations. By using these equations, we derive recurrence relations and some formulas of our numbers. Moreover, we give two algorithms for computation our numbers. We also give some combinatorial applications, further remarks on our numbers and their generating functions.
36 citations
TL;DR: In this article, a pseudoperfect number is defined as the sum of all of its proper divisors, except for one of them, referred to as the redundant divisor.
27 citations
1 Dec 1984
TL;DR: In this article, it was shown that computing s(N) is equivalent to factoring N in the following sense: there is a random polynomial-time algorithm that, given n, produces the prime factorization of n, and s(n) can be easily computed given the factorization.
Abstract: Let N be a positive integer, and let s(N) denote the sum of the positive integral divisors of N. We show computing s(N) is equivalent to factoring N in the following sense: there is a random polynomial time algorithm that, given s(N), produces the prime factorization of N, and s(N) can be easily computed given the factorization of N. We show that the same sort of result holds for sk(N), the sum of the k-th powers of divisors of N. We give three new examples of problems that are in Gill's complexity class BPP: {perfect numbers}, {multiply perfect numbers}, and {amicable pairs}. These are the first “natural” candidates for BPP - RP.
27 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2017 | 4 |
| 2016 | 3 |
| 2015 | 13 |
| 2014 | 1 |
| 2013 | 4 |