#!/usr/bin/env python3

# Challenge 150
#
# TASK #2 > Square-free Integer
# Submitted by: Mohammad S Anwar
# Write a script to generate all square-free integers <= 500.
#
# In mathematics, a square-free integer (or squarefree integer) is an integer
# which is divisible by no perfect square other than 1. That is, its prime
# factorization has exactly one factor for each prime that appears in it. For
# example, 10 = 2 x 5 is square-free, but 18 = 2 x 3 x 3 is not, because 18 is
# divisible by 9 = 3**2.
#
# Example
# The smallest positive square-free integers are
#     1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...

from sympy import factorint

def is_squarefree(n):
    factors = factorint(n)
    for k in factors.values():
        if k > 1:
            return False
    return True

out = [n for n in range(1, 501) if is_squarefree(n)]
print(", ".join(map(str, out)))