Kata

The numbers 12, 63 and 119 have something in common related with their divisors and their prime factors, let's see it.

Numbers PrimeFactorsSum(pfs)        DivisorsSum(ds)              Is ds divisible by pfs
12         2 + 2 + 3 = 7         1 + 2 + 3 + 4 + 6 + 12 = 28            28 / 7 = 4,  Yes
63         3 + 3 + 7 = 13        1 + 3 + 7 + 9 + 21 + 63 = 104         104 / 13 = 8, Yes
119        7 + 17 = 24           1 + 7 + 17 + 119 = 144                144 / 24 = 6, Yes

There is an obvius property you can see: the sum of the divisors of a number is divisible by the sum of its prime factors.

We need the function ds_multof_pfs() that receives two arguments: nMin and nMax, as a lower and upper limit (inclusives), respectively, and outputs a sorted list with the numbers that fulfill the property described above.

We represent the features of the described function:

ds_multof_pfs(nMin, nMax) -----> [n1, n2, ....., nl] # nMin ≤ n1 < n2 < ..< nl ≤ nMax

Let's see some cases:

ds_multof_pfs(10, 100) == [12, 15, 35, 42, 60, 63, 66, 68, 84, 90, 95]

ds_multof_pfs(20, 120) == [35, 42, 60, 63, 66, 68, 84, 90, 95, 110, 114, 119]

Enjoy it!!