Practice Arithmetic and Tricky with the exercise "Sum of divisors"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Arithmetic

Statement

Goal

You have to print the sum of divisors of all the numbers from 1 to n.
It’s superfast when you know the trick but you have to find it.
For example if n=4, lets define d(n) the set of the divisors of n:
* d(1)={1},
* d(2)={1,2},
* d(3)={1,3},
* d(4)={1,2,4}.
And their sum is 1+1+2+1+3+1+2+4=15.
Look carefully at the divisors to find the trick.

Input

A single number n

Output

The sum

Constraints

1⩽n⩽100000

Example

Input

Output

Solve it

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