adapt to update sieves for additive functions

internal/lib/sieve/common.go

@@ -16,14 +16,18 @@ 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 {
+				if additive {
+					sieve[i] += sieve[q]
+				} else {
 					sieve[i] *= sieve[q]
 				}
 			}
+		}
 
 		if p*q >= n {
 			break

internal/lib/sieve/divisors.go

@@ -55,7 +55,7 @@ func Divisors(n uint, x uint, buflen uint) chan uint {
 				sieve[i*j] = pow(i*j, x) + sieve[j]
 			}
 
-			updateMultiples(sieve, i, n)
+			updateMultiples(sieve, i, n, false)
 			ch <- sieve[i]
 		}
 	}()

internal/lib/sieve/primeOmega.go

@@ -16,21 +16,6 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
 package sieve
 
-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 {
-			if i%(p*q) != 0 {
-				sieve[i] += sieve[q]
-			}
-		}
-
-		if p*q >= n {
-			break
-		}
-	}
-}
-
 func updatePowers(sieve []uint, p uint, n uint) {
 	for q := p; p*q < n; q *= p {
 		sieve[p*q] = 1 + sieve[q]
@@ -60,7 +45,7 @@ func PrimeOmega(n uint, multiplicity bool, buflen uint) chan uint {
 				updatePowers(sieve, i, n)
 			}
 
-			primeOmegaUpdateMultiples(sieve, i, n)
+			updateMultiples(sieve, i, n, true)
 			ch <- sieve[i]
 		}
 	}()

internal/lib/sieve/radical.go

@@ -59,7 +59,7 @@ func Radical(n uint, buflen uint) chan uint {
 				sieve[i*j] = sieve[i]
 			}
 
-			updateMultiples(sieve, i, n)
+			updateMultiples(sieve, i, n, false)
 			ch <- sieve[i]
 		}
 	}()