def solve():
sieve(12000)
cache = [0,0,0,0] + [None] * 12001
qty = 0
for d in xrange(4, 12001):
cache[d] = twixtQty(d) - sum(cache[div] for div in divisors(d)
if div != d)
qty += cache[d]
return qty
def solve():
sieve(10**6)
mdrs = [None] * 10**6
mdrs[0] = 0 # to emulate the omission of 1 from factorizations
accum = 0
for n in xrange(2, 10**6):
val = max(droot(d) + mdrs[n // d - 1] for d in divisors(n) if d != 1)
accum += val
mdrs[n-1] = val
return accum
def test_divisors_1(self):
d = eulerlib.divisors(1)
assert d == [1], 'Divisors should be 1'
def test_divisors_0(self):
d = eulerlib.divisors(0)
assert d == []
def test_divisors_1001(self):
d = eulerlib.divisors(1001)
assert d == [1, 7, 11, 13, 77, 91, 143, 1001]
def test_divisors_17(self):
d = eulerlib.divisors(17)
assert d == [1, 17], 'Divisors should be 1 and 17.'
def test_divisors_neg10(self):
d = eulerlib.divisors(-10)
assert d == [1, 2, 5, 10], 'Divisors should be 1, 2, 5, 10'