Pseudoperfect numbers

The proper divisors of a number n are all the positive divisors of n
that are smaller than n. For instance, the proper divisors of 20 are 1,
2, 4, 5, and 10. In this problem, we will say that a number is
pseudoperfect if it can be obtained by adding up some of (or all) its
proper divisors. For instance, 20 is pseudoperfect, because
1 + 4 + 5 + 10 = 20.

Write a program that, for every given number n,

- if n has more than 15 proper divisors, prints how many it has;

- if n has 15 or less proper divisors, tells if n is pseudoperfect or
  not.

Input

Input consists of several strictly positive natural numbers.

Output

For every given n, print its number of proper divisors, if this is
larger than 15. Otherwise, tell if n is pseudoperfect or not. Follow the
format of the example.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T11:58:43.011Z

© Jutge.org, 2006–2026.
https://jutge.org
