def generate_divisors(n):
factors = to_powers(factorize(n))
nfactors = len(factors)
f = [0] * nfactors
while True:
yield reduce(lambda x, y: x*y,
[factors[x][0]**f[x] for x in range(nfactors)], 1)
i = 0
while True:
f[i] += 1
if f[i] <= factors[i][1]:
break
f[i] = 0
i += 1
if i >= nfactors:
return
def divs(n):
powers = to_powers(factorize(n))
# powers = [(a,x), (b,y), (c,z)] so that n = a^x * b^y * c^z
divisors_count = reduce(lambda x, y: x*y, (f[1]+1 for f in powers))
return divisors_count