refactor updating prime powers

internal/lib/sieve/primeOmega.go

@@ -16,7 +16,7 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
 package sieve
 
-func primeOmegaUpdateMultiples(sieve []uint, p uint, n uint, multiplicity bool) {
+func primeOmegaUpdateMultiples(sieve []uint, p uint, n uint) {
 	for q := p; ; q *= p {
 		// omega(a*b) = omega(a) + omega(b) if gcd(a,b) = 1
 		for i := 2 * q; i < n; i += q {
@@ -28,10 +28,12 @@ func primeOmegaUpdateMultiples(sieve []uint, p uint, n uint, multiplicity bool)
 		if p*q >= n {
 			break
 		}
-
-		if multiplicity {
-			sieve[p*q] = 1 + sieve[q]
 	}
+}
+
+func updatePowers(sieve []uint, p uint, n uint) {
+	for q := p; p*q < n; q *= p {
+		sieve[p*q] = 1 + sieve[q]
 	}
 }
 
@@ -54,7 +56,11 @@ func PrimeOmega(n uint, multiplicity bool, buflen uint) chan uint {
 			}
 
 			sieve[i] = 1
-			primeOmegaUpdateMultiples(sieve, i, n, multiplicity)
+			if multiplicity {
+				updatePowers(sieve, i, n)
+			}
+
+			primeOmegaUpdateMultiples(sieve, i, n)
 			ch <- sieve[i]
 		}
 	}()