import time
from primes import get_primes, divisors, m_r
START = time.time()
SIZE = 10**6 * 5
LIM = 10**5
primes = get_primes(SIZE)
div308 = divisors(308)
results = []
for p in primes:
if len(results) > LIM: break
if not any([m_r(div * p + 1) for div in div308]):
results.append(p)
print results[LIM - 2] * 308, len(results)
for repetition in xrange(10):
resultSet = set(results)
for index, a in enumerate(results):
if a * results[0] > results[LIM]: break
for bIndex in xrange(index + 1):
b = results[bIndex]
p = a * b
if a * b > results[LIM]: break
if not any([m_r(div * p + 1) for div in div308]):
if len(filter(lambda x: x not in resultSet,
divisors(p)[1:-1])) == 0:
import time
from primes import divisors, factor, pfactor_gen
START = time.time()
SIZE = 10**6
factors = pfactor_gen(SIZE)
for i in xrange(2,SIZE,2):
if sum(divisors(i)) % i == i/2:
print i, factor(i)
print "Time Taken:", time.time() - START
"""
2: 1,3,7,15,31,65,129
3: 1,4,10,40,121,364
5: 1,6,31,156,781,3906
p(2) = 3/2 -> 1 1/2
p(24) = (13 * 4)/8 = 6 1/2
p(4320) = (63 * 40 * 6) = 3 1/2
-> 2^4 * 3^3 * 5 * 7
4320 = 2^5 * 3^3 * 5
2 [2]
24 [2, 2, 2, 3]
4320 [2, 2, 2, 2, 2, 3, 3, 3, 5]
4680 [2, 2, 2, 3, 3, 5, 13]
def presents(n):
s = 0
for divisor in divisors(n):
if n / divisor <= 50:
s += divisor
return s * 11
def num_divisors(n):
return sum(1 for _ in primes.divisors(n))
from primes import divisors
count = 19423091
fronta = range(1, count + 1)
c = 0
while len(fronta) > 1:
c += 1
to_remove = []
l = len(fronta)
for d in divisors(l):
if d > 1:
x = d
while x <= l:
to_remove.append(fronta[x - 1])
x += d
to_remove = set(to_remove)
new = []
for f in fronta:
if f not in to_remove:
new.append(f)
fronta = new
print(c, len(fronta))
if (len(fronta) < 100):
print fronta
print(fronta, c)
for m in xrange(1,1000):
print m
for n in xrange(1,m):
h1 = m**2 - n**2
w = 2*m*n
d2 = m**2 + n**2
if h1*2 + w*2 > SIZE:
break
for i in xrange(2):
if w % 4 != 0:
h1, w = w,h1
continue
for a in divisors(w/4):
for c in divisors(w/ (4*a)):
b = w / (4*a * c)
if a <= b:
break
h2 = (a**2 - b**2) * c
d1 = (a**2 + b**2) * c
if h2 > h1:
continue
if isSquare((h1+h2)**2 + (w/2)**2):
print "AB:", h1, "BD:", w, "BC:", d1, "Mult:", c
if (h1*2 + w + d1*2) <= SIZE:
total += h1*2 + w + d1 * 2
import time, math
from primes import divisors, totient
START = time.time()
LIM = 10**15
sumz = 0
for m in xrange(2,20):
for n in xrange(1,30):
num_sum = 0
for d in divisors(n):
num_sum += totient(n/d) * math.factorial(m*d) / math.factorial(d)**m
num_sum /= m*n
if num_sum < LIM:
sumz += num_sum
else:
break
if n == 1:
break
print "Answer:", sumz
print "Time Taken:", time.time() - START
"""
Congratulations, the answer you gave to problem 281 is correct.
You are the 611th person to have solved this problem.
t(1,n) = 1
import time
from primes import divisors, factor, pfactor_gen
START = time.time()
SIZE = 10**6
factors = pfactor_gen(SIZE)
for i in xrange(2, SIZE, 2):
if sum(divisors(i)) % i == i / 2:
print i, factor(i)
print "Time Taken:", time.time() - START
"""
2: 1,3,7,15,31,65,129
3: 1,4,10,40,121,364
5: 1,6,31,156,781,3906
p(2) = 3/2 -> 1 1/2
p(24) = (13 * 4)/8 = 6 1/2
p(4320) = (63 * 40 * 6) = 3 1/2
-> 2^4 * 3^3 * 5 * 7
4320 = 2^5 * 3^3 * 5
2 [2]
24 [2, 2, 2, 3]
4320 [2, 2, 2, 2, 2, 3, 3, 3, 5]
4680 [2, 2, 2, 3, 3, 5, 13]
26208 [2, 2, 2, 2, 2, 3, 3, 7, 13]
for m in xrange(1, 1000):
print m
for n in xrange(1, m):
h1 = m**2 - n**2
w = 2 * m * n
d2 = m**2 + n**2
if h1 * 2 + w * 2 > SIZE:
break
for i in xrange(2):
if w % 4 != 0:
h1, w = w, h1
continue
for a in divisors(w / 4):
for c in divisors(w / (4 * a)):
b = w / (4 * a * c)
if a <= b:
break
h2 = (a**2 - b**2) * c
d1 = (a**2 + b**2) * c
if h2 > h1:
continue
if isSquare((h1 + h2)**2 + (w / 2)**2):
print "AB:", h1, "BD:", w, "BC:", d1, "Mult:", c
if (h1 * 2 + w + d1 * 2) <= SIZE:
total += h1 * 2 + w + d1 * 2
import time, math
from primes import divisors, totient
START = time.time()
LIM = 10**15
sumz = 0
for m in xrange(2, 20):
for n in xrange(1, 30):
num_sum = 0
for d in divisors(n):
num_sum += totient(n / d) * math.factorial(
m * d) / math.factorial(d)**m
num_sum /= m * n
if num_sum < LIM:
sumz += num_sum
else:
break
if n == 1:
break
print "Answer:", sumz
print "Time Taken:", time.time() - START
"""
Congratulations, the answer you gave to problem 281 is correct.
You are the 611th person to have solved this problem.
t(1,n) = 1
t(2,n) = OEIS series here: https://oeis.org/A003239
def d(n):
proper_divisors = divisors(n)[:-1]
return sum(proper_divisors)