adapt to update sieves for additive functions

internal/lib/sieve/common.go

@@ -16,12 +16,16 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
 package sieve
 
-func updateMultiples(sieve []uint, p uint, n uint) {
+func updateMultiples(sieve []uint, p uint, n uint, additive bool) {
 	for q := p; ; q *= p {
 		// sieve[a*b] = sieve[a] * sieve[b] if gcd(a,b) = 1
 		for i := 2 * q; i < n; i += q {
 			if i%(p*q) != 0 {
-				sieve[i] *= sieve[q]
+				if additive {
+					sieve[i] += sieve[q]
+				} else {
+					sieve[i] *= sieve[q]
+				}
 			}
 		}