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#include <stdio.h>
/* Time: 2m5.335s */
typedef struct
{
int p;
int np;
} prime_factor;
/* factorize n, return number of prime factors */
int get_prime_factors(int n, prime_factor *pf)
{
int npf = 0;
int np;
if (n <= 1)
return 0;
if (n % 2 == 0) {
pf[0].p = 2;
np = 0;
while (n % 2 == 0) {
n /= 2;
np++;
}
pf[0].np = np;
npf = 1;
}
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0) {
pf[npf].p = i;
np = 0;
while (n % i == 0) {
n /= i;
np ++;
}
pf[npf].np = np;
npf++;
}
}
if (n > 1) {
pf[npf].p = n;
pf[npf].np = 1;
npf++;
}
return npf;
}
int get_factors_from_pf(prime_factor pf[], int npf, int factors[])
{
factors[0] = 1;
int idx = 1;
for (int i = 0; i < npf; i++) {
int nidx = idx;
for (int j = 0; j < pf[i].np; j++) {
for (int k = 0; k < idx; k++) {
factors[nidx+k] = factors[nidx+k-idx] * pf[i].p;
}
nidx += idx;
}
idx = nidx;
}
return idx;
}
int get_all_factors(int n, int factors[])
{
prime_factor pf[100];
int npf = get_prime_factors(n, pf);
return get_factors_from_pf(pf, npf, factors);
}
int isprime(int n)
{
if (n < 2 || n % 2 == 0)
return 0;
for (int i = 3; i * i <= n; i += 2) {
if (n % i == 0)
return 0;
}
return 1;
}
int main()
{
long long sum = 3; /* n can be 1, 2 */
int factors[10000];
prime_factor pf[100];
for (int i = 6; i <= 100000000; i += 4) { /* n must be 4k+2 */
int isok = 1;
int npf = get_prime_factors(i, pf);
for (int j = 0; j < npf; j++) {
if (pf[j].np > 1) {
isok = 0;
break;
}
}
if (!isok)
continue;
int nf = get_factors_from_pf(pf, npf, factors);
for (int j = 0; j < nf; j++) {
int t = factors[j] + i/factors[j];
if (!isprime(t)) {
isok = 0;
break;
}
}
if (isok) {
sum += i;
}
}
printf("%lld\n", sum);
}
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