In [1]:

    

from euler import get_factors


    

In [2]:

    

get_factors(20)


    

    
Out[2]:





[2, 2, 5]

In [3]:

    

def terse(x):
    f = {}
    for i in x:
        if i not in f:
            f[i] = 0
        f[i] += 1
    return f


    

In [4]:

    

terse(get_factors(20))


    

    
Out[4]:





{2: 2, 5: 1}

In [5]:

    

def get_terse_primes(x):
    primes = {}
    for i in range(2, x + 1):
        p = terse(get_factors(i))
        for key in p:
            if key not in primes:
                primes[key] = 0
            if p[key] > primes[key]:
                primes[key] = p[key]
    return primes


    

In [6]:

    

get_terse_primes(20)


    

    
Out[6]:





{2: 4, 3: 2, 5: 1, 7: 1, 11: 1, 13: 1, 17: 1, 19: 1}

In [7]:

    

def product_terse_primes(x):
    product = 1
    primes = get_terse_primes(x)
    for prime in primes:
        product *= prime ** primes[prime]
    return product


    

In [8]:

    

%timeit product_terse_primes(20)
product_terse_primes(20)


    

    




10000 loops, best of 3: 77.8 us per loop






    
Out[8]:





232792560