The following is a refactoring of the Python code found here for computing the arithmetic derivative.

from sympy import factorint

def f(n):
    result = factorint(n)
    result = result.items()
    result = [int(n*e/p) for p, e in result]
    result = sum(result)
    result = result if n > 1 else 0
    return result 

It can be shown that the arithmetic derivative of a primer number to the power of itself will be a fixed point. Feel free to scrutinize the proof if you think that is where the issue lies.

A051674 is the sequence of primes to the power of themselves in the usual ordering of the primes. Among them is 827240261886336764177, but when I call the above function on it I do not get the correct result:

>>> f(827240261886336764177)
827240261886336827392

In fact, tabulating all of the listed sequence members evaluated by f reveals that entries before that work, and entries after that break.

So it seems that the numbers becoming too large might be a problem. Why does this function fail on these larger cases?

CodePudding user response：

If you are dealing with integers, try to only use integer operations. Since in the line

result = [int(n*e/p) for p, e in result]

n, e and p are integers (int types), simply write n*e//p instead of int(n*e/p).