def get_first_house(target, start, verbose=True):
"""
Given a target and starting value, find the first integer n greater than
or equal to start such that the sum of divisors of n is at least as big as
target
"""
for i in count(start):
num_presents = divisor_sigma(i)
if num_presents >= target:
return i
if verbose and (i % 1000) == 0:
print('Calculating sum of divisors for {}'.format(i))
def base_program_shortcut(data, initial_0):
# this gets the sum of divisors for some large number
ip = int(data[0].split()[1])
program = data[1:]
register = [0] * 6
register[0] = initial_0
idx = 0
while 0 <= register[ip] < len(program):
idx += 1
if register[5] == 3:
break
line = program[register[ip]]
register = eval(line + 'register)')
register[ip] += 1
big_number = register[1]
return divisor_sigma(big_number, 1)
def test_divisor_sigma():
assert [divisor_sigma(k) for k in range(1, 12)] == \
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12]
assert [divisor_sigma(k, 2) for k in range(1, 12)] == \
[1, 5, 10, 21, 26, 50, 50, 85, 91, 130, 122]
assert divisor_sigma(23450) == 50592
assert divisor_sigma(23450, 0) == 24
assert divisor_sigma(23450, 1) == 50592
assert divisor_sigma(23450, 2) == 730747500
assert divisor_sigma(23450, 3) == 14666785333344
a = Symbol("a", prime=True)
b = Symbol("b", prime=True)
j = Symbol("j", integer=True, positive=True)
k = Symbol("k", integer=True, positive=True)
assert divisor_sigma(a**j*b**k) == (a**(j + 1) - 1)*(b**(k + 1) - 1)/((a - 1)*(b - 1))
assert divisor_sigma(a**j*b**k, 2) == (a**(2*j + 2) - 1)*(b**(2*k + 2) - 1)/((a**2 - 1)*(b**2 - 1))
assert divisor_sigma(a**j*b**k, 0) == (j + 1)*(k + 1)
m = Symbol("m", integer=True)
k = Symbol("k", integer=True)
assert divisor_sigma(m)
assert divisor_sigma(m, k)
assert divisor_sigma(m).subs(m, 3**10) == 88573
assert divisor_sigma(m, k).subs([(m, 3**10), (k, 3)]) == 213810021790597
assert summation(divisor_sigma(m), (m, 1, 11)) == 99
def test_divisor_sigma():
assert [divisor_sigma(k) for k in range(1, 12)] == \
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12]
assert [divisor_sigma(k, 2) for k in range(1, 12)] == \
[1, 5, 10, 21, 26, 50, 50, 85, 91, 130, 122]
assert divisor_sigma(23450) == 50592
assert divisor_sigma(23450, 0) == 24
assert divisor_sigma(23450, 1) == 50592
assert divisor_sigma(23450, 2) == 730747500
assert divisor_sigma(23450, 3) == 14666785333344
m = Symbol("m", integer=True)
k = Symbol("k", integer=True)
assert divisor_sigma(m)
assert divisor_sigma(m, k)
assert divisor_sigma(m).subs(m, 3**10) == 88573
assert divisor_sigma(m, k).subs([(m, 3**10), (k, 3)]) == 213810021790597
assert summation(divisor_sigma(m), (m, 1, 11)) == 99
def test_divisor_sigma():
assert [divisor_sigma(k) for k in range(1, 12)] == \
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12]
assert [divisor_sigma(k, 2) for k in range(1, 12)] == \
[1, 5, 10, 21, 26, 50, 50, 85, 91, 130, 122]
assert divisor_sigma(23450) == 50592
assert divisor_sigma(23450, 0) == 24
assert divisor_sigma(23450, 1) == 50592
assert divisor_sigma(23450, 2) == 730747500
assert divisor_sigma(23450, 3) == 14666785333344
m = Symbol("m", integer=True)
k = Symbol("k", integer=True)
assert divisor_sigma(m)
assert divisor_sigma(m, k)
assert divisor_sigma(m).subs(m, 3**10) == 88573
assert divisor_sigma(m, k).subs([(m, 3**10), (k, 3)]) == 213810021790597
assert summation(divisor_sigma(m), (m, 1, 11)) == 99
