**Problems**

**Problem(s) 1. An integer can be the sum of reciprocals of **
**distinct**
** integers (do you see how these ones come from perfect numbers?):**

**Can you make up some more? And how about triply-perfect numbers producing:**

** **
** , with distinct unit fractions **
** **

**Write a program that would enable you to find some triply-perfect, quadruply-perfect numbers, etc (with a view to finding sums of distinct unit fractions that add up to (1), (2), 3, 4, 5, ... )**

**Problem 2. Prove that no integer can be expressed as a sum of reciprocals of distinct **
**primes**
**.**

**Problem 3. Prove **
** is never an integer.**