def f(val, min_, max_):
"""
#>>> f(Fraction(1, 2), 2, 80)
0
>>> f(Fraction(1, 2), 2, 45)
3
"""
A = []
tmp = 0
for v in reversed(range(min_, max_ + 1)):
tmp += Fraction(1, v * v)
A.insert(0, tmp)
next_number = {}
i = min_
while i < max_:
j = i + 1
while len(set(factorize(j)) - set([2,3,5,7])) != 0:
j += 1
if j <= max_:
next_number[i] = j
i = j
queue = [(val, min_)]
index = 0
counter = 0
while index < len(queue):
val, now = queue[index]
print now, index
remain = A[now - min_]
if val == remain or val == 0:
counter += 1
if val == remain or val == 0:
counter += 1
elif 0 < val < remain:
if val + val > remain:
val = remain - val
if now < max_:
queue.append((val, next_number[now]))
queue.append((val - Fraction(1, now * now), next_number[now]))
index += 1
return counter
def Di(n):
result = 1
for p, x in Counter(factorize(n)).iteritems():
result *= (p ** (x + 1) - 1)/(p - 1)
return result
