add divisor summatory function

cmd/divisor.go

@@ -0,0 +1,78 @@
+/*
+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"
+	"log"
+	"math/big"
+
+	"github.com/spf13/cobra"
+)
+
+// TODO: expand to work for different sigmas
+func divisorSummatory(n *big.Int) *big.Int {
+	// employing Dirichlet's hyperbola method
+	sqrt := new(big.Int).Sqrt(n)
+
+	total := big.NewInt(0)
+	for x := big.NewInt(1); x.Cmp(sqrt) <= 0; x.Add(x, big.NewInt(1)) {
+		z := new(big.Int).Div(n, x)
+		total.Add(total, z)
+	}
+
+	total.Mul(total, big.NewInt(2))
+
+	sqrt.Exp(sqrt, big.NewInt(2), nil)
+	total.Sub(total, sqrt)
+
+	return total
+}
+
+func divisorSum(cmd *cobra.Command, args []string) {
+	for _, arg := range args {
+		n, ok := new(big.Int).SetString(arg, 10)
+		if !ok {
+			log.Print("invalid input " + arg)
+		}
+
+		d := divisorSummatory(n)
+		fmt.Println(d)
+	}
+}
+
+// divisorCmd represents the divisor command
+var divisorCmd = &cobra.Command{
+	Use:   "divisor N [N ...]",
+	Short: "Compute the divisor summatory function",
+	Long:  `Compute the divisor summatory function.`,
+	Run:   divisorSum,
+}
+
+func init() {
+	sumCmd.AddCommand(divisorCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// divisorCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// divisorCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+}

cmd/sum.go

@@ -0,0 +1,42 @@
+/*
+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 (
+	"github.com/spf13/cobra"
+)
+
+// sumCmd represents the sum command
+var sumCmd = &cobra.Command{
+	Use:   "sum",
+	Short: "Compute summatory functions",
+	Long:  `Compute summatory functions.`,
+}
+
+func init() {
+	rootCmd.AddCommand(sumCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// sumCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// sumCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+}