Question: For any positive integer n , ( n ) denotes the sum of the positive divisors of n . A number n N is said

For any positive integer n , (n) denotes the sum of the positive divisors of n.

A number nN is said to be "perfect" if (n)=2n.

(For example, since the positive divisors of 6 are 1, 2, 3 and 6 and since 1+2+3+6=12= 2(6), 6 is therefore a perfect number).

Suppose p is a prime number with the property that the number 2p1 is also a prime.

Prove that n=2p1(2p1) is also a perfect number.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Wolfram language (Mathmatica Programming) (a) Write a function which takes as input a positive integer n and returns the sum of all proper divisors of n. Show how your function works for the...

Q:

A perfect number is a positive integer n that equals the sum of all divisors less than n . For example, 6 is a perfect number because 6 = 1 + 2 + 3 . Perfect numbers are related to Mersenne primes in...

Q:

Write an algorithm that determines how many positive in - tegers evenly divide the positive integer n . The algorithm should return the number of divisors ( not the actual divisors ) . For example, 4...

Q:

Background: Loop statements allow us to run the same block of code repeatedly, with the chance to use different values for variables each time as the accumulated effects pile up. Lists and strings...

Q:

I am so confused with loops, thank you in advance! What can and can't I use or do? Many built-in functions in python would make our tasks so trivial that you wouldn't really be learning, just...

Q:

Allowed: variables, assignments, selection statements (if-elif-else), loops (of course!), indexing/slicing. basic operators: +, -, *, 7, 11, %, ==, !=,, =, in, not in, and, or, not. when you need to...

Q:

Hello, can someone answer all parts? Thank you. What can and can't I use or do? Many built-in functions in python would make our tasks so trivial that you wouldn't really be learning, just "phoning...

Q:

Hello, can someone answer all parts? Thank you. What can and can't I use or do? Many built-in functions in python would make our tasks so trivial that you wouldn't really be learning, just "phoning...

Q:

Need help with this array exercise on python Please Write the following functions. See the commented out part of the program for expected results. Also, make sure your functions don't modify the...

Q:

1. Pi Estimation, The value of Pie can be estimated from the expression: 2/Pi = root(2)/2 root(2 +root (2))/2 root(2 + root(2 + root(2)))/2 In a script file, write a MATLAB program that determine Pi...

Q:

Assume that you are the owner of a small neighborhood bakery serving hundreds of customers in your area. Identify the kinds of customer information you would like your firms CRM system to capture....

Q:

The IT company is a small chain of distributors of good quality laptops, softwares, web sites Apps etc. . Within each category, the company offers a wide variety of products, with a great many...

Q:

Mod 7 . 8 , and 9 ) 3 Help A long - term liability should be reported as a current liability in a classified balance sheet if the long - term debt Multiple Choice Is secured by adequate collateral....

Q:

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.