def IsPractical(n):
if n % 2 != 0: return False
#D = divisors(n)
#if sum(D) == n*2: return True
lg = log(n) / log(2)
if lg == int(lg): return True
F = RetFact(n)
S = sorted(list(set(F)))
for k in range(1, len(S)):
a = S[k]
f = S[:k]
v = 1
for fn in f:
v *= fn**F.count(fn)
w = sum(divisors(v)) + 1
if a > w:
print a, w, n, S
return False
print "Yes", n
return True
def IsPractical(n):
if n%2 != 0: return False
#D = divisors(n)
#if sum(D) == n*2: return True
lg = log(n)/log(2)
if lg == int(lg): return True
F = RetFact(n)
S = sorted(list(set(F)))
for k in range(1,len(S)):
a = S[k]
f = S[:k]
v = 1
for fn in f:
v*= fn**F.count(fn)
w = sum(divisors(v)) + 1
if a > w:
print a, w,n,S
return False
print "Yes",n
return True
def cntpowers(x):
z = RetFact(x)
S = set(z)
summ = 0
for SS in S:
summ += z.count(SS)
return summ
def cntpowers(x):
z = RetFact(x)
S = set(z)
summ = 0
for SS in S:
summ += z.count(SS)
return summ
# x + y = xy/n
#
# 1/x = 1/n - 1/y
#
#
#
from Functions import RetFact, IsPrime
n = 1260 #500000000
maxx = 0
for n in xrange(10**8, 10**9): #15000):
if IsPrime(n): continue
x = RetFact(n**2)
s = set(x)
facts = []
for f in s:
facts.append(x.count(f) + 1)
m = 1
for f in facts:
m *= f
m += 1
m /= 2
if m > maxx:
maxx = m
print "!!!!!", n, ":", m
else:
print n, ":", m
if maxx > 4000000: print "Over 4 Mil!", n, m
print
print "# of solutions for", n, "is", maxx
return False
return True
d = divisors(120120)
x=[]
s=set(x)
s2=set(x)
for x in d:
z = RetFact(x)
S = set(z)
summ = 0
for SS in S:
summ += z.count(SS)
if summ == 4:
print x
# for x in d:
# z = RetFact(x)
# two = z.count(2)
# zz = x/(2**two)
# zzz = 3**(two+1)*zz
# if zzz>(120120/4):
# print x,two, zz,z
# for i in xrange(126,2,-1):
# s = set([d[i]])
# x + y = xy/n
#
# 1/x = 1/n - 1/y
#
#
#
from Functions import RetFact, IsPrime
n = 1260 #500000000
maxx = 0
for n in xrange(10**8, 10**9): #15000):
if IsPrime(n):continue
x = RetFact(n**2)
s = set(x)
facts = []
for f in s:
facts.append(x.count(f)+1)
m=1
for f in facts:
m*=f
m+=1
m/=2
if m>maxx:
maxx=m
print "!!!!!",n,":",m
else:
print n,":",m
if maxx>4000000:print "Over 4 Mil!",n,m
print
print "# of solutions for",n, "is", maxx