Please help with 22! **Exercise 11: Number Theory Functions**For this exercise, we are asked to find the number-theoretic functions \( \tau(n) \), \( \sigma(n) \), \( \lambda(n) \), \( \mu(n) \), \( \omega(n) \), and \( \phi(n) \) for the following integers:- 2250- 199- 286936650- \( 22! \)**Annotations on the Image:**1. **\( 22! \) is circled**: This indicates particular interest or focus on the factorial of 22.2. **Extra notes (handwritten)**: - A calculation is provided for \( 22 \times 2 \times 3 \times 3 \times 4 \times 2 \). - On the right side, there’s a division calculation showing \( \frac{18}{4} = 4.5 \).These notes might relate to partial calculations relevant to understanding the properties or decompositions of the number in question when exploring factorials or prime factorizations.**Overview of Functions**:- **\( \tau(n) \)**: Total number of divisors of \( n \).- **\( \sigma(n) \)**: Sum of the divisors of \( n \).- **\( \lambda(n) \)**: Carmichael function of \( n \), the smallest positive integer \( m \) such that \( a^m \equiv 1 \pmod{n} \) for all integers \( a \) coprime to \( n \).- **\( \mu(n) \)**: Möbius function of \( n \), which is used in number theory with values: \( 0, -1, 1 \).- **\( \omega(n) \)**: Number of distinct prime factors of \( n \).- **\( \phi(n) \)**: Euler's totient function, representing the count of integers up to \( n \) that are coprime to \( n \).The task involves using these functions to derive properties about the provided integers to illustrate concepts in number theory.

Answered: Image /qna-images/answer/c9381540-56be-4b1a-9819-d1210d488738.jpg

Answered: 11. Find 7(n), o(n), X(n), µ(n), w(n),…

11. Find 7(n), o(n), X(n), µ(n), w(n), and ø(n) for the following integers.' 2250 • 199 • 286936650 2.3.3,4. 2 • 22! oloment havin

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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