long sigma(long k, long* primes) {
long* factors = pfactors(k, primes);
long prod = 1;
long i;
for(i = 0; factors[i] != 0; i += 2) {
long num = ipow(factors[i], factors[i+1]+1)-1;
long den = factors[i]-1;
prod *= num/den;
}
free(factors);
return prod;
}
// Generate a random LCG "multiplier" which will give a full period for a
// "modulus" of `m`.
//
// http://en.wikipedia.org/wiki/Linear_congruential_generator
// > [...] the LCG will have a full period for all seed values if and only if:
// > [...]
// > 2. `a` - 1 is divisible by all prime factors of `m`,
// > 3. `a` - 1 is a multiple of 4 if `m` is a multiple of 4.
//
// This function generates a sufficient `a`.
int mul(int m) {
int a = m * 0.75;
bool sufficient = false;
bool m_divis_4 = m % 4 == 0;
while (!sufficient) {
a = (a + 1) % (m - 1) + 1; // skip a == 0
sufficient = true;
unsigned int* factors = pfactors(m);
int i;
for (i = 1; sufficient && i < factors[i]; i++) {
sufficient = (a - 1) % factors[i] == 0;
}
free(factors);
sufficient = sufficient && (!m_divis_4 || (a - 1) % 4 == 0);
}
return a;
}
