refactor updating multiples into separate common function

internal/lib/sieve/common.go

@@ -0,0 +1,32 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package sieve
+
+func updateMultiples(sieve []uint, p uint, n uint) {
+	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 p*q >= n {
+			break
+		}
+	}
+}

internal/lib/sieve/divisors.go

@@ -30,24 +30,6 @@ func pow(base uint, exp uint) uint {
 	return result
 }
 
-func updateMultiples(sieve []uint, x uint, p uint, n uint) {
-	for q := p; ; q *= p {
-		// sigma_x(a*b) = sigma_x(a) * sigma_x(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
-		}
-
-		// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
-		sieve[p*q] = pow(p*q, x) + sieve[q]
-	}
-}
-
 /*
 Divisors computes sigma_x(k) for k=1 to n, where sigma_x is the divisor sum function. x sets the power each divisor is raised to.
 */
@@ -68,7 +50,12 @@ func Divisors(n uint, x uint, buflen uint) chan uint {
 			}
 
 			sieve[i] = pow(i, x) + 1
-			updateMultiples(sieve, x, i, n)
+			for j := i; i*j < n; j *= i {
+				// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
+				sieve[i*j] = pow(i*j, x) + sieve[j]
+			}
+
+			updateMultiples(sieve, i, n)
 			ch <- sieve[i]
 		}
 	}()