def tester(n):
def _key(z):
return z[1][1] #len(z[1])
euler_tools.write_primes(int(n))
primes = euler_tools.read_primes()
with euler_tools.Watch():
print(prime_divisor(9917, primes))
import euler_tools
euler_tools.write_primes(12001)
PRIMES = sorted(euler_tools.read_primes())
def gcd(a, b):
r = a % b
while r != 0:
a = b
b = r
r = a % b
return b
def coprime_2(n, m):
return gcd(n, m) == 1
def totients(n):
t = list(range(1, n+1))
for p in PRIMES:
m = 1
while m*p <= n:
t[m*p-1] *= (1-1/p)
m += 1
return [int(_t) for _t in t]
CP = {}
def coprime(n, m):
try:
#tester(1e6)
#euler_tools.write_primes(D)
#with euler_tools.Watch():
#print(euler_tools.prime_divisors(12345678))
#euler_tools.write_primes(int(1e6))
#with euler_tools.Watch():
# print(euler_tools.prime_divisors(12345678))
D = int(1e6) + 1
euler_tools.write_primes(int(1e6))
primes = euler_tools.read_primes()
#with euler_tools.Watch():
# x = [euler_tools.totient(i, primes) for i in range(2, D)]
#print(x)
#print(sum(x))
lst = list(range(D))
for p in primes:
r = p - 1
lst[p] = r
lst[p + p::p] = [i / p * (p - 1) for i in lst[p + p::p]]
print(sum(lst[2:]))
import decimal
import euler_tools
euler_tools.write_primes(int(1e5))
PRIMES = euler_tools.read_primes()
def ppt(n):
def powers(k):
_powers = []
for p in PRIMES:
num = p**k
if num < n:
_powers.append(num)
else:
break
return _powers
squares = powers(2)
cubes = powers(3)
tesseracts = powers(4)
ppts = []
for square in squares:
for cube in cubes:
for tesseract in tesseracts:
x = square + cube + tesseract
if x < n:
ppts.append(x)
return set(ppts)
