def prime_divisors(n):
try:
return PDS[n]
except KeyError:
#with euler_tools.Watch('PRIME DIVISORS %s' % n):
pds = euler_tools.prime_divisors(n)
PDS[n] = pds
return pds
def keys(n):
dice = sieve(n)
p = 1
for m in range(1, n + 1):
o = sum([d for d in dice[:m] if d == 1])
if p + 1 == o:
print(m, o, euler_tools.prime_divisors(m))
p = o
return None
def replace(factorization, factor, limit):
_factorization = copy.deepcopy(factorization)
for i in range(2, factor):
factorization[factor] = 0
pds = euler_tools.prime_divisors(i)
for pd in pds:
factorization[pd] += 1
print(factor, i, pds, factorization, d(factorization),
d(_factorization))
if 2 * limit < d(factorization):
return factorization, True
else:
factorization = copy.deepcopy(_factorization)
return _factorization, False
def prime_divisor(i, primes):
s = time.time()
pds = euler_tools.prime_divisors(i, primes)
e = time.time() - s
return pds, e
def check_x(x, nds):
xds = euler_tools.prime_divisors(x**3 - 1)
for nd in nds:
if nd not in xds:
return False
return True
def check(n):
for x in check_n(n):
print(x, euler_tools.prime_divisors_2(n),
euler_tools.prime_divisors(x**3 - 1))
def combin(n, k):
return int(fact(n) / (fact(k) * fact(n - k)))
def product(x):
p = 1
for _x in x:
p *= _x
return p
def num_divisors(num_primes):
return 1 + sum([combin(num_primes, n) for n in range(1, num_primes + 1)])
# def pseudo_sqrt(n):
# index = len(all_divisors(n))/2-1
print(euler_tools.prime_divisors(3102), 3102**0.5)
print(PRIMES, product(PRIMES), product(PRIMES)**0.5)
#p = product(PRIMES)
#d = euler_tools.all_divisors(p)
#print(d, len(d), d.index(42))
print(num_divisors(len(PRIMES)) / 2 - 1)
if x.is_integer() and y.is_integer(
) and p < p_max and not seen[(x, y)]:
print(a, b, c, x, y, p, area)
triples += p
seen[(x, y)] = True
else:
triples += 0
else:
triples += 0
#print(max_p, max_p/p_max)
m += 1
return triples
N = 5
P = 1e6
#triples = pythag_triples(N, P)
#print(triples)
print(coprime(516309057, 894260792))
print(coprime(516309057, 1032607092))
print(coprime(894260792, 1032607092))
print(euler_tools.prime_divisors(516309057))
print(euler_tools.prime_divisors(894260792))
print(euler_tools.prime_divisors(1032607092))