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