## Arithmetic Derivative

### Problem 484

The **arithmetic derivative** is defined by

`p'`= 1 for any prime`p`- (
`ab`)`'`=`a'b`+`ab'`for all integers`a`,`b`(Leibniz rule)

For example, 20`'` = 24

Find ∑ **gcd**(`k`,`k'`) for 1 < `k` ≤ 5·10^{15}

Note: **gcd**(`x`,`y`) denotes the greatest common divisor of `x` and `y`.