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1007 - Mathematically Hard
 PDF (English) Statistics Forum
 Time Limit: 2 second(s) Memory Limit: 64 MB

Mathematically some problems look hard. But with the help of the computer, some problems can be easily solvable.

In this problem, you will be given two integers a and b. You have to find the summation of the scores of the numbers from a to b (inclusive). The score of a number is defined as the following function.

score (x) = n2, where n is the number of relatively prime numbers with x, which are smaller than x

For example,

For 6, the relatively prime numbers with 6 are 1 and 5. So, score (6) = 22 = 4.

For 8, the relatively prime numbers with 8 are 1, 3, 5 and 7. So, score (8) = 42 = 16.

Now you have to solve this task.

# Input

Input starts with an integer T (≤ 105), denoting the number of test cases.

Each case will contain two integers a and b (2 ≤ a ≤ b ≤ 5 * 106).

# Output

For each case, print the case number and the summation of all the scores from a to b.

3

6 6

8 8

2 20

Case 1: 4

Case 2: 16

Case 3: 1237

# Note

Euler's totient function  applied to a positive integer n is defined to be the number of positive integers less than or equal to n that are relatively prime to n is read "phi of n."

Given the general prime factorization of , one can compute  using the formula

Problem Setter: Jane Alam Jan
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