41 lines
1.1 KiB
Go
41 lines
1.1 KiB
Go
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/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package lib
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import (
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"math/big"
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)
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// TODO: expand to work for different sigmas
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func DivisorSummatory(n *big.Int) *big.Int {
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// employing Dirichlet's hyperbola method
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sqrt := new(big.Int).Sqrt(n)
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total := big.NewInt(0)
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for x := big.NewInt(1); x.Cmp(sqrt) <= 0; x.Add(x, big.NewInt(1)) {
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z := new(big.Int).Div(n, x)
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total.Add(total, z)
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}
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total.Mul(total, big.NewInt(2))
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sqrt.Exp(sqrt, big.NewInt(2), nil)
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total.Sub(total, sqrt)
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return total
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}
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