def divisors(n):
factors = RetFact(n)
factors.append(1)
fact=[]
l = len(factors)
for z in xrange(2,l+1):
y = combinations(factors,z)
for yy in y:
yyy = list(yy)
#print yyy
s1 = 1
for yyyy in yyy:
s1*=yyyy
fact.append(s1)
fact.append(1)
fact = sorted(list(set(fact)))
#print fact
return fact
def divisors(n):
factors = RetFact(n)
factors.append(1)
fact = []
l = len(factors)
for z in xrange(2, l + 1):
y = combinations(factors, z)
for yy in y:
yyy = list(yy)
#print yyy
s1 = 1
for yyyy in yyy:
s1 *= yyyy
fact.append(s1)
fact.append(1)
fact = sorted(list(set(fact)))
#print fact
return fact
def PhiPrimes(n):
totfacts = []
n1 = n - 1
totfacts = RetFact(n1)
allfactsfound = False
while allfactsfound == False:
newfactfound = False
for m in totfacts:
o = RetFact(m - 1)
for p in o:
if p < 2: continue
if not p in totfacts:
totfacts.append(p)
newfactfound = True
if newfactfound == False: allfactsfound = True
return list(set(totfacts))
def PhiPrimes(n):
totfacts=[]
n1 = n-1
totfacts = RetFact(n1)
allfactsfound = False
while allfactsfound == False:
newfactfound = False
for m in totfacts:
o = RetFact(m-1)
for p in o:
if p<2:continue
if not p in totfacts:
totfacts.append(p)
newfactfound = True
if newfactfound == False: allfactsfound = True
return list(set(totfacts))
lim = 100000 # 10000
# F = FactorSieve(100**3)
a, b, c = 0, 0, 0
cnt = 0
for a in xrange(2, lim, 3):
x = 8 * a * a * a + 15 * a * a + 6 * a - 1
if x % 27 == 0:
x /= 27 # x = b*b*c
y = RetFact(x)
y.append(1)
y = set(y)
# print "!",a,y
for z in y:
b = z
c = int(x / (b ** 2))
# print "!!",x,":",a,b,c
if x == b * b * c:
if a + b + c <= 1000: # 110000000:
cnt += 1
# print a,b,c
print "Number of Cardano Triplets <=", lim, "is", cnt
print "Process time is", time() - st