#!/usr/bin/env python
import primes
from bisect import bisect_left, bisect_right
from pe_tools import nCr, approx_int_sqrt
below_n = 10 ** 8
def num_coprimes_with(p, relevant_primes):
max_p = below_n / p
assert p <= max_p
return bisect_right(relevant_primes, max_p) - bisect_left(relevant_primes, p)
if __name__ == "__main__":
relevant_primes = sorted(list(filter((lambda x: x < below_n), primes.get_huge_prime_set())))
print sum(
num_coprimes_with(n, relevant_primes)
for n in relevant_primes[: bisect_right(relevant_primes, approx_int_sqrt(below_n))]
)
#!/usr/bin/env python
from primes import is_prime, get_huge_prime_set
primes = get_huge_prime_set()
factors = [0] * (10 ** 6 + 1)
def set_factors():
for i in range(len(factors)):
if i < 4 or is_prime(i):
factors[i] = [i]
continue
for p in primes:
if i % p == 0:
factors[i] = [p, i/p]
break
set_factors()
def compute_factors(n):
from itertools import chain
from pe_tools import approx_int_sqrt
if is_prime(n):
return [n]
s = approx_int_sqrt(n)
for p in chain(primes, xrange(max(primes), s, 2)):
if n % p == 0:
return [n] + get_factors(n/p)
raise Exception("Failed to factor {}".format(n))
