k-perfect numbers#3233
It is known that a number is called perfect if it equals the sum of all its positive divisors except itself. For example, the first perfect number is 6 = 1 + 2 + 3. Now, let us state this more rigorously. We consider the function:
A number is perfect if and only if \sigma(n) - n = 0.
A number is called -perfect if |\sigma(n) - n| = k. Thus, -perfect numbers, for example, are and . Your task is to find the number of -perfect numbers in the interval [l, r].
The first line of the input file contains the number of tests (1 \leq t \leq 100\,000). Each test consists of one line containing three integers , , and , separated by single spaces (1 \leq l \leq r \leq 10^6, 0 \leq k \leq 10^9).
For each test case, output a string containing the number of -perfect numbers in the interval [l, r].
Esempio 1