def find_consecutive(howmany):
latest = [] # factors of the previous consecutive numbers
for n in itertools.count(2):
facn = factors.factor_count(n).items()
if len(facn) != howmany:
latest = []
continue
latest.append(set(facn))
latest = latest[-howmany:]
## are they distinct?
all_factors = functools.reduce(set.union, latest)
if len(all_factors) == howmany**2:
return n - howmany + 1
def count_divisors(n):
fdict = factors.factor_count(n)
if not fdict:
return 1
return functools.reduce(operator.mul, (c+1 for c in fdict.values()))