Week 5: Thursday
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Q1. (50)

A positive integer n is square-free if it is not divisible by any perfect
square, except 1.

For example, 44 is not square-free as it is divisible by 4 = 2*2; 6 is
square-free.

The Mobius function M(n) for a positive integer n is defined as follows:

M(n) =  0 if n is not square-free
M(n) = +1 if n is square-free with even number of prime factors
M(n) = -1 if n is square-free with odd  number of prime factors

For example, M(44) = 0 as it is not square-free; M(6) = +1 as it has 2 prime
factors (2 and 3); M(30) = -1 as it has three prime factors (2, 3 and 5).

Write a program that inputs a positive integer and outputs its Mobius function.
Your program should implement the following two functions (other than the main):
	1. int square_free(int n): returns 1 if n is square_free, 0 otherwise
	2. int mobius(int n): returns the mobius function of n

Q2. (50)

Euclid numbers E(n) are positive integers of the form E(n) = P(n) + 1, where
P(n) is the primorial of n.  Primorial of n is defined as the product of first
n prime numbers (prime numbers start from 2).  For example, P(0) = 1 (base
case); P(1) = 2; P(2) = 6 (2 x 3); P(5) = 2310 (2 x 3 x 5 x 7 x 11).

Write a program that prints all the Euclid numbers until the first composite
Euclid number is reached. Your program should implement the following two
functions (other than the main):
	1. int isprime(int n): returns 1 if n is prime, 0 otherwise
    2. int primorial(int n): returns the primorial of n