move sieves to subpackage

internal/lib/sieve/primeOmega.go

@@ -0,0 +1,63 @@
+/*
+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 primeOmegaUpdateMultiples(sieve []uint, p uint, n uint, multiplicity bool) {
+	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
+		}
+
+		if multiplicity {
+			sieve[p*q] = 1 + sieve[q]
+		}
+	}
+}
+
+/*
+PrimeOmegaSieve computes omega(k) for k=1 to n, where omega is the prime omega function. If multiplicity is true, factors are counted with multiplicity.
+*/
+func PrimeOmegaSieve(n uint, multiplicity bool, buflen uint) chan uint {
+	sieve := make([]uint, n)
+	for i := uint(0); i < n; i++ {
+		sieve[i] = 0
+	}
+
+	ch := make(chan uint, buflen)
+	go func() {
+		defer close(ch)
+		for i := uint(0); i < n; i++ {
+			if i == 0 || i == 1 || sieve[i] != 0 {
+				ch <- sieve[i]
+				continue
+			}
+
+			sieve[i] = 1
+			primeOmegaUpdateMultiples(sieve, i, n, multiplicity)
+			ch <- sieve[i]
+		}
+	}()
+
+	return ch
+}