Distinct Primes Factors ¶

The prime omega function $\omega(n)$ counts the number of distinct prime factors of $n$. SageMath provides this function through the PARI/GP interface, but we can also just look at the length of the output of the built-in factor function.

See problem 3 for information on implementing a factorization function.

In [1]:

from itertools import count

def omega(n):
    return len(factor(n))


for n in count(1):
    if all(omega(n+k) == 4 for k in (0,1,2,3)):
        break

n

Out[1]:

Relevant sequences¶

Number of distinct prime factors: A001221

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