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5. Let 02(n) be the sum of the squares of the divisors of n 0₂(n) = Σd². din Make a guess at a general formula for O(n), the sum of the kth powers of the divisors of n.

5. Let 02(n) be the sum of the squares of the divisors of n 0₂(n) = Σd². din Make a guess at a general formula for O(n), the sum of the kth powers of the divisors of n.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem 5: Sum of Squares of Divisors** Let \( \sigma_2(n) \) be the sum of the squares of the divisors of \( n \). \[ \sigma_2(n) = \sum_{d \mid n} d^2 \] **Exercise:** Make a guess at a general formula for \( \sigma_k(n) \), the sum of the \( k^{th} \) powers of the divisors of \( n \).
Transcribed Image Text:**Problem 5: Sum of Squares of Divisors** Let \( \sigma_2(n) \) be the sum of the squares of the divisors of \( n \). \[ \sigma_2(n) = \sum_{d \mid n} d^2 \] **Exercise:** Make a guess at a general formula for \( \sigma_k(n) \), the sum of the \( k^{th} \) powers of the divisors of \( n \).
Expert Solution
Step 1: Sum of series obtained.

It is given that

sigma subscript 2 left parenthesis n right parenthesis space equals space sum from d divided by n to blank of d squared ,    then

sigma subscript k left parenthesis n right parenthesis space equals sum from d divided by n to blank of d to the power of k


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