A k-hyperperfect number is a natural number n for which the equality n = 1 + k(σ(n) − n − 1) holds, where σ(n) is the divisor function (i.e., the sum of all positive divisors of n).
%Example
sigma(6) = 1 + 2 + 3 + 6 = 12
%for k=1
1 + 1*(12-6-1) = 1 + 5 = 6
%Example
sigma(325) = 1 + 5 + 13 + 25 + 65 + 325 = 434
%for k=3
1 + 3*(434-325-1) = 1 + 3*108 = 324
Given a number x, return the xth Hyperperfect number (serial/order wise) and corresponding k value.
P.S - Check the test suite for banned functions. More functions might be added later to prevent hard coded solutions.
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