#include <bits/stdc++.h>
using namespace std;
const int N = 40000;
bool notPrime[N];
vector<int> primes;
int divisorsNo(int w) {
int ret = 1;
for (int prime : primes) {
if (w < prime) {
break;
}
int cnt = 0;
while (w % prime == 0) {
w /= prime;
cnt++;
}
ret *= (cnt + 1);
}
if (w > 1) {
ret *= 2;
}
return ret;
}
int compForGivenA(int a, int n) {
int d = n / a - 1;
if (d <= 1) return 0;
if (d == 2) return 0;
return divisorsNo(d) - 2 - (d % 2 == 0);
}
void sieve(int w) {
for (int i = 2; i * i <= w; i++) {
if (!notPrime[i]) {
primes.push_back(i);
for (int j = 2 * i; (long long)j * j <= w; j += i) {
notPrime[j] = true;
}
}
}
}
int main() {
int n;
scanf("%d", &n);
if (n <= 5) {
printf("0\n");
return 0;
}
sieve(n);
long long ans = 0;
for (int i = 1; i * i <= n; i++) {
if (n % i == 0) {
ans += compForGivenA(i, n);
if (i != n / i) {
ans += compForGivenA(n / i, n);
}
}
}
printf("%lld\n", ans);
return 0;
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | #include <bits/stdc++.h> using namespace std; const int N = 40000; bool notPrime[N]; vector<int> primes; int divisorsNo(int w) { int ret = 1; for (int prime : primes) { if (w < prime) { break; } int cnt = 0; while (w % prime == 0) { w /= prime; cnt++; } ret *= (cnt + 1); } if (w > 1) { ret *= 2; } return ret; } int compForGivenA(int a, int n) { int d = n / a - 1; if (d <= 1) return 0; if (d == 2) return 0; return divisorsNo(d) - 2 - (d % 2 == 0); } void sieve(int w) { for (int i = 2; i * i <= w; i++) { if (!notPrime[i]) { primes.push_back(i); for (int j = 2 * i; (long long)j * j <= w; j += i) { notPrime[j] = true; } } } } int main() { int n; scanf("%d", &n); if (n <= 5) { printf("0\n"); return 0; } sieve(n); long long ans = 0; for (int i = 1; i * i <= n; i++) { if (n % i == 0) { ans += compForGivenA(i, n); if (i != n / i) { ans += compForGivenA(n / i, n); } } } printf("%lld\n", ans); return 0; } |
English