bracket.py

#!/usr/bin/python3
import sys

def primes(n):
    candidates = range(2,n+1)

    primes = []

    while candidates:
        prime = candidates[0]
        primes.append(prime)
        candidates = list(filter(lambda x:x%prime, candidates[1:]))

    return len(primes), n == 1 or primes[-1] == n

def factor(n):
    factors = []
    i = 2
    while i * i <= n:
        while n % i == 0:
            n = n // i
            factors.append(i)
        i = i + 1
    factors.append(n)
    return [factor for factor in factors if factor != 1]

def get_brackets(n, include_primality=False):
    symbols = [n]

    n_is_prime = None

    while True:
        for index, symbol in enumerate(symbols):
            if type(symbol) == int:
                if symbol == 1:
                    symbols[index] = ''
                    break
                prime_count, is_prime = primes(symbol)
                if n_is_prime is None:
                    n_is_prime = is_prime
                #if is_prime:
                    #p_arg = Number(symbol.prime_count())
                    #symbols = symbols[:index] + ['<', p_arg, '>'] + symbols[index+1:]
                    #break
                #else:
                    #symbols = symbols[:index] + [Number(n) for n in factor(symbol.value)] + symbols[index+1:]
                    #break
                symbols = symbols[:index] + (
                    ['<', prime_count, '>']
                    if is_prime
                    else factor(symbol)
                ) + symbols[index+1:]
                break
        else:
            break
    brackets = ''.join(symbols)
    return (brackets, n_is_prime) if include_primality else brackets

if __name__ == '__main__':
    n = int(sys.argv[1] if len(sys.argv) > 1 else sys.stdin.read())
    print(get_brackets(n))