# 829. Consecutive Numbers Sum

## Description

Given an integer n, return the number of ways you can write n as the sum of consecutive positive integers.

Example 1:

Input: n = 5
Output: 2
Explanation: 5 = 2 + 3


Example 2:

Input: n = 9
Output: 3
Explanation: 9 = 4 + 5 = 2 + 3 + 4


Example 3:

Input: n = 15
Output: 4
Explanation: 15 = 8 + 7 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5


Constraints:

• 1 <= n <= 109

## Solutions

• class Solution {
n <<= 1;
int ans = 0;
for (int k = 1; k * (k + 1) <= n; ++k) {
if (n % k == 0 && (n / k + 1 - k) % 2 == 0) {
++ans;
}
}
return ans;
}
}

• class Solution {
public:
n <<= 1;
int ans = 0;
for (int k = 1; k * (k + 1) <= n; ++k) {
if (n % k == 0 && (n / k + 1 - k) % 2 == 0) {
++ans;
}
}
return ans;
}
};

• class Solution:
def consecutiveNumbersSum(self, n: int) -> int:
n <<= 1
ans, k = 0, 1
while k * (k + 1) <= n:
if n % k == 0 and (n // k + 1 - k) % 2 == 0:
ans += 1
k += 1
return ans


• func consecutiveNumbersSum(n int) int {
n <<= 1
ans := 0
for k := 1; k*(k+1) <= n; k++ {
if n%k == 0 && (n/k+1-k)%2 == 0 {
ans++
}
}
return ans
}

• function consecutiveNumbersSum(n: number): number {
let ans = 0;
n <<= 1;
for (let k = 1; k * (k + 1) <= n; ++k) {
if (n % k === 0 && (Math.floor(n / k) + 1 - k) % 2 === 0) {
++ans;
}
}
return ans;
}