mathtools/cmd/divisor.go

/*
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"
	"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 {
			cmd.PrintErrln("invalid input " + arg)
			continue
		}

		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.

For each argument n, compute D(n) = d(1) + d(2) + d(3) + ... + d(n), where d(n) is the number of divisors of n.`,
	Args: cobra.MinimumNArgs(1),
	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")
}