add prime-omega command

cmd/primeOmega.go

@@ -0,0 +1,106 @@
+/*
+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 cmd
+
+import (
+	"fmt"
+
+	"github.com/spf13/cobra"
+)
+
+var primeOmegaN uint
+
+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 primeOmegaSieve(n uint) chan uint {
+	sieve := make([]uint, n)
+	for i := uint(0); i < n; i++ {
+		sieve[i] = 0
+	}
+
+	ch := make(chan uint)
+	go func() {
+		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)
+			ch <- sieve[i]
+		}
+
+		close(ch)
+	}()
+
+	return ch
+}
+
+func primeOmega(cmd *cobra.Command, args []string) {
+	ch := primeOmegaSieve(primeOmegaN)
+	for i := 0; ; i++ {
+		v, ok := <-ch
+		if !ok {
+			break
+		}
+
+		if i == 0 {
+			continue
+		}
+
+		fmt.Println(v)
+	}
+}
+
+// primeOmegaCmd represents the primeOmega command
+var primeOmegaCmd = &cobra.Command{
+	Use:   "prime-omega -n N",
+	Short: "",
+	Long:  ``,
+	Run:   primeOmega,
+}
+
+func init() {
+	sieveCmd.AddCommand(primeOmegaCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// primeOmegaCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// primeOmegaCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	primeOmegaCmd.Flags().UintVarP(&primeOmegaN, "limit", "n", 0, "upper limit")
+	primeOmegaCmd.MarkFlagRequired("limit")
+}