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TASK #1 - Farey Sequence
You are given a positive number, $n.
Write a script to compute the Farey Sequence of the order $n, defined as:
is the sequence of completely reduced fractions, between 0 and 1,
which have numerators and denominators less than or equal to n,
arranged in order of increasing size).
Example 1:
Input: $n = 5
Output: 0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1.
Example 2:
Input: $n = 7
Output: 0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7,
3/5, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 1/1.
Example 3:
Input: $n = 4
Output: 0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1.
MY NOTES: ok. Pretty easy. Will need a way to reduce fractions, and a way of
storing that reduced fraction in a set (storing "Num/Denom" should do it).
TASK #2 - Moebius Number
You are given a positive number $n.
Write a script to generate the Moebius Number for the given number,
definition: For any positive integer n, define moeb(n) as:
moeb(n) = +1 if n is a square-free positive integer with an even
number of prime factors.
moeb(n) = 1 if n is a square-free positive integer with an odd
number of prime factors.
moeb(n) = 0 if n has a squared prime factor.
Example 1:
Input: $n = 5
Output: -1
Example 2:
Input: $n = 10
Output: 1
Example 3:
Input: $n = 20
Output: 0
MY NOTES: ok. Slightly tricky.
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