Purchase Solution

A perfect number

Not what you're looking for?

Ask Custom Question

A perfect number is an integer that equals the sum of its proper positive factors. For example, the proper positive factors of 6 are 1, 2, and 3. Since 1 + 2 + 3 = 6, we refer to 6 as a perfect number. Similarly, 28 = 1 + 2 + 4 + 7 + 14, so it is also a perfect number. I intend to show that the sum of the reciprocals of the factors of a perfect number is equal to 2. Notice that 1 + 1/2 + 1/3 + 1/6 = 2 and 1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28 = 2.

Attachments
Purchase this Solution
Solution Summary

A perfect number is depicted.

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Combinatorial Study of φ(n), d(n) and σ(n).

    Prove that if n is a perfect number , then ∑1/d = 2.

  • Primes and divisibility word problem

    The smallest number (other than one) that is a perfect square, a perfect cube, and a perfect fifth power is calculated.

  • conditions of perfect market

    Perfect competition: An industry made up of a large number of small firms, each selling homogeneous (identical) products to a large number of buyers. Agricultural products are the closest form of pure or perfect competition.

  • Three characteristics of perfect competition

    Explain each of them and support your answer with some APA Reference The three characteristics of perfect competition are a large number of small firms, identical products, and perfect knowledge of prices and technology (1).

  • Perfect Numbers

    85979 Perfect Numbers An integer n is called k-perfect if σ(n) = kn (note that a perfect number is 2-perfect). (a) Show that 120 = 23? ? ? 3 ? ? ? 5 is 3-perfect. (b) Show that if n is 3-perfect and gcd(3, n) = 1, then 3n is 4-perfect.

  • Number Theory Perfect Square

    For p = 17, and for m = -1, n^2 = -1 - (-1)*17 = 16 which is a perfect square For p = 19, there is no n^2. The number theory for perfect squares are determined.

  • Market Structure Classification

    There are definitely quite a few grocery stores in your city, but the number is definitely a lot less than the number of grocery shoppers. Thus this does not look at a perfect competition. - No barriers to entry/exit.

  • Mathematics - Algebra

    A Complete, Neat and Step-by-step Solution is provided in the attached file.

  • Explain the Proof Step-by-step : If n is not a perfect square, then n^(1/2) is irrational.

    35502 Explain the Proof Step-by-step : Irrational Function Recall that a perfect sqaure is a natural number n such that n = (k^2), for some natural number k. Theorem. If the natural number n is not a perfect square, then n^(1/2) is irrational.

View More Related Solutions