Radical of a number

radical.py

from collections import defaultdict

def radical(n):
  primes = [True] * (n + 1)
  primes[0] = primes[1] = False
  for i in range(n + 1):
    if primes[i]:
      j = 2
      while i * j <= n:
        primes[i * j] = False
        j += 1
  res = 1
  for i in range(n + 1):
    if primes[i] and n % i == 0:
      res *= i
  return res

N = 100
buckets = defaultdict(list)
for i in range(1, N + 1):
  buckets[radical(i)].append(i)
radicals = sorted(buckets.keys(), key = lambda i: -len(buckets[i]))
for i in radicals:
  vals = ", ".join(map(str, buckets[i]))
  print(f"{i} => {vals}")