# Double Arithmetic Derivative

$\Large \frac{d}{dx} n \neq 0?$

In calculus, when you take the derivative of a constant you get zero as an answer. In number theory, there is something called the arithmetic derivative which allows you to differentiate a number and get a nonzero answer. The arithmetic derivative works as follows.

Where $n'$ denotes the arithmetic derivative of $n$:

$p' = 1$ for all primes $p$

$(ab)'=a'b+ab'$

$0'=1'=0$

For example, $6'=(2\times3)'=(2')(3)+(2)(3')=(1)(3)+(2)(1)=5$

The double arithmetic derivative, denoted by $n''$, is simply defined by $n''=(n')'$.

Find the sum of all positive integers $n<100$ such that $n''=1$

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