def divisor_sum(n):
divisors = [1]
for i in range(2, approx_int_sqrt(n)):
if n % i == 0:
divisors.append(i)
divisors.append(n / i)
return sum(divisors)
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))
def get_answer():
for n in range(1, approx_int_sqrt(max_total)):
for m in range(n+1, max_total/n, 2):
if gcd(m,n) != 1:
continue
a = m*m - n*n
b = 2*m*n
c = m*m + n*n
if a + b + c > max_total:
break
assert(a*a + b*b == c*c)
for k in count(1):
ka = k*a
kb = k*b
kc = k*c
if ka + kb + kc > max_total:
break
assert ka**2 + kb**2 == kc**2
triples[ka+kb+kc] += 1
print "{}".format(len(filter(lambda x: x == 1, triples)))
#!/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))]
)
