move to lib

internal/lib/divisor.go

@@ -0,0 +1,40 @@
+/*
+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 lib
+
+import (
+	"math/big"
+)
+
+// 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
+}