How to approach this problem?

#1

Can you please guide me how to solve this problem.

#2

Hello @HemantKumar,

For a given integer x,
you need to find the number of pairs <a,b> such that gcd(a,b)=1.
So, you need to find the number of pairs <a, x!/a> such that a ϵ {factors of x!}.

OR

It follows a pattern. I can give you a hint.
The task is to factor n! into a and b such that gcd(p,q)=1 and p<q. so we calculate the number of distinct primes in n!
Let prime factorisation of n!= (p1)^x1 * (p2)^x2 …(pk)^xk
now for each i, (pi)^xi can either go in p or q. hence 2^k ways. but as we want p<q. therefore only 2^(k-1) ways.

Hope, this would help.

#3

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