An interesting problem on number Theory(help) : Uva12716 — GCD XOR

Правка en1, от rsazid99, 2017-12-10 01:08:21

Given an integer N, find how many pairs (A, B) are there such that: gcd(A, B) = A xor B where 1 ≤ B ≤ A ≤ N. Here gcd(A, B) means the greatest common divisor of the numbers A and B. And A xor B is the value of the bitwise xor operation on the binary representation of A and B. Input The first line of the input contains an integer T (T ≤ 10000) denoting the number of test cases. The following T lines contain an integer N (1 ≤ N ≤ 30000000). Output For each test case, print the case number first in the format, ‘Case X:’ (here, X is the serial of the input) followed by a space and then the answer for that case. There is no new-line between cases. Explanation Sample 1: For N = 7, there are four valid pairs: (3, 2), (5, 4), (6, 4) and (7, 6).

Sample Input

2

7

20000000

Sample Output

Case 1: 4

Case 2: 34866117

Link:https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4454

i am not getting any idea, how to solve this problem. Thanks in Advance :)

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en1 Английский rsazid99 2017-12-10 01:08:21 1105 Initial revision (published)