def solve_twodigit():
for n in xrange(99*99, 1, -1):
## if n < 9000:
## break
if ispalindrome(n) and not isprime(n):
# print 'checking',n
for x in factors(n):
if x <= 99 and x >= 10 and n / x > 10 and n / x < 99:
print n, ':', x, '*', n / x
break
i = 1
s = 0
while True:
s = s + i
i += 1
yield s
## demo
#c=0
#for x in tris():
# if c >= 7:
# break
# print '%2i: %s' % (x, ','.join(map(str, [f for f in factors(x)])))
# c+=1
m = 0
n = 1
t = tris()
while m < 500:
c = t.next()
m = max(m, count_factors(c))
n+=1
if n % 200==0:
print n
print '%2i: %s' % (c, ','.join(map(str, [f for f in factors(c)])))
# 11800
# 12000
# 12200
#76576500
though it is known that the greatest number that cannot be expressed as
the sum of two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the
sum of two abundant numbers.
"""
import psyco
psyco.full()
import fast_prime as fp
mrange = 28124
abunds = {}
for i in range(1, mrange):
fs = [f for f in fp.factors(i)][:-1]
s = sum(fs)
if s > i:
abunds[i] = 0
nsum = []
for n in range(1, mrange):
found = False
for k in abunds:
if n - k in abunds:
found = True
break
if not found:
nsum.append(n)
print len(nsum), sum(nsum)
# 1456 abundants, sum = 4179871
c = 1
vals = []
while c < 10000:
vals.append(count_factors(c))
c += 1
return vals
def sols():
c = 1
vals = []
while c < 10000:
vals.append(solutions(c))
c += 1
return vals
s = time.time()
sols()
print "solutions in", time.time() - s
s = time.time()
cfs()
print "count factors in", time.time() - s
else:
m = 10000
v = dict((n, solutions(n)) for n in range(1, m+1))
v2 = dict((n, count_factors(n)) for n in range(1,m+1))
for i in v:
if v[i] != v2[i]:
print '%-4i: %-3i%i' % (i, v[i], v2[i])
print ' ', ','.join(map(str, [f for f in factors(i)]))
print ' ', ','.join(map(str, [f for f in psolutions(i)]))
"""
2007-12-14
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 317584931803?
>>> for x in factors(13195):
... if isprime(x):
... print '%i,'%x ,
5, 7, 13, 29,
"""
from fast_prime import factors, isprime
for x in factors(317584931803):
if isprime(x):
print "%i," % x,
# 1, 67, 829, 1459, 3919