Let d(n) be the sum of positive integers divisors of number n and ϕ(n) the quantity of integers in the interval [0,n] such that these integers are coprime with n. For instance d(6)=12 and ϕ(7)=6.
Determine if the set of the integers n such that, d(n)⋅ϕ(n) is a perfect square, is finite or infinite set. Divisorsnumber theoryalgebra