The Lagarias arithmetic derivative 
is defined for integers such that the derivative of a prime number is 1: 
. It also satisfies the Leibniz formula, which resembles the product rule of calculus:
is defined for integers such that the derivative of a prime number is 1: . It also satisfies the Leibniz formula, which resembles the product rule of calculus:
For example, the arithmetic derivative of 15 is 
. The Leibniz formula also implies that 
.
. The Leibniz formula also implies that . Write a function to compute the arithmetic derivative of a natural number.
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