Question

For any positive integer n, let d(n) denotes the number of positive divisors of n; and let ϕ(n) denote the number of elements from the set {1, 2,….. n} that are coprime to n.

(For example, d(12) = 6 and ϕ(12) = 4.)

Find the smallest positive integer n such that d(ϕ(n)) = 2017.

Answer 1

d(ϕ(n)) = 2017

As 2017 is a prime number

where P₁, P₂ , ……P_n are the prime factors of n

Let ϕ(n) = t

d(t) = 2017 => for minimum we have t is also minimum