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#!/usr/bin/env python3
def is_achilles_number(num):
'''Determine if this number is an achilles numbers'''
# Get the prime factors of the number
factors = {}
i = 2
while num > 1:
if num % i == 0:
num /= i
if i in factors:
factors[i] += 1
else:
factors[i] = 1
else:
i += 1
# If there is only one prime factor, it is not an achilles number
if len(factors) == 1:
return False
# Get a list of unique powers
powers = set(factors.values())
# It's also not an achilles number if any of the powers were 1, or the
# powers are all the same (a perfect sqaure)
if 1 in powers or len(powers) == 1:
return False
# Finally, the greatest common divisor of these numbers has to be one
for i in range(2, min(powers)+1):
if all(x % i == 0 for x in powers):
return False
return True
def main():
'''Find the first 20 achilles numbers'''
solutions = []
num = 2
# Get the first 20 achilles numbers
while len(solutions) < 20:
if is_achilles_number(num):
solutions.append(num)
num += 1
# Print the list
print(*solutions, sep=', ')
if __name__ == '__main__':
main()
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