Take a positive integer `n` and factor it into a product of primes, then replace multiplication in that product with addition. eg: 6 = 2 * 3 becomes 5 = 2 + 3. Here's the plot of the number you get from that sum (vertical axis) for each of the originally factored numbers `n` (horizontal axis). Notice that many of these sums are equal to the original number. All primes are guaranteed to have their prime-sum equal to themselves because they are their own single prime factor

This procedure must have a name, but I don't know what it is