Kata

If we have an integer of n digits, d1d2d3d4d5....dn, we define the following scores:

score_prod = 1d₁ + 2d₂ + 3d₃ + 4d₄ + 5d₅ + .... + nd_n

score_pow = 1^d1 + 2^d2 + 3^d3 + 4^d4 + 5^d5 + .... + n^dn

We want to find the integers that its score_pow multiplied by a certain integer k is divisible by the sum of the divisors of score_prod

In the sum of the divisors, 1 and the score_prod themselves are addens.

In this kata you have to create the function find_int(), that will receive three arguments:

• The extreme values of a range (a, b), a as a start value and b as an upper limit, both included.

• An integer k such that 1 <= k <= 100

The function will output a tuple with the amount of found integers and an array with the sorted integers that fulfill the above condition.

Let's see some cases:

test.describe("Basic Tests")
a = 100
b = 200
k = 1
find_int(a, b, k) == (7, [100, 110, 120, 135, 195, 197, 200])

a = 500
b = 700
k = 2
find_int(a, b, k) == (18, [500, 510, 531, 532, 535, 553, 570, 611, 612, 614, 617, 625, 627, 631, 634, 671, 695, 699])

a = 500
b = 700
k = 3
find_int(a, b, k) == (16, [501, 511, 532, 535, 553, 560, 571, 581, 613, 614, 617, 620, 625, 644, 645, 674])

a = 500
b = 700
k = 4
find_int(a, b, k) == (30, [500, 510, 531, 532, 534, 535, 553, 558, 570, 600, 611, 612, 614, 615, 617, 625, 627, 631, 634, 636, 637, 640, 671, 675, 679, 682, 692, 693, 695, 699])

For the tests always a < b.

Enjoy it!!