AtCoder Beginner Contest 169, D. Div Game short code

"Divide by $ p ^ 1, p ^ 2, p ^ 3, \ ldots $ and record the number of cracks, Stop recording the number of times and divide as much as you can divide by $ p $ " Is repeated with $ p = 2, 3, 5, 7, 9, \ ldots, \ sqrt {N} $. Add 1 if there are still prime numbers left. Like.

N = int(input())
n, p, score = N, 2, 0
while p ** 2 <= N:
  e = 1
  while n % (p ** e) == 0:
    n //= (p ** e)
    score += 1
    e += 1
  else:
    while n % p == 0:
      n //= p
    p = p + 1 if p == 2 else p + 2
else:
  if n != 1:
    score += 1
print(score)

A little shorter

N = int(input())
n, p, score = N, 2, 0
while p ** 2 <= N:
  e = 1
  while n % (p ** e) == 0:
    n //= (p ** e)
    score += 1
    e += 1
  else:
    while n % p == 0:
      n //= p
    p += 2 - (p == 2)
else:
  score += n > 1
print(score)

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