78 lines
1.7 KiB
Go
78 lines
1.7 KiB
Go
/*
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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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func pow(base uint, exp uint) uint {
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result := uint(1)
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for exp > 0 {
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if exp%2 == 1 {
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result *= base
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}
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exp >>= 1
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base *= base
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}
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return result
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}
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func updateMultiples(sieve []uint, x uint, p uint, n uint) {
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for q := p; ; q *= p {
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// sigma_x(a*b) = sigma_x(a) * sigma_x(b) if gcd(a,b) = 1
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for i := 2 * q; i < n; i += q {
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if i%(p*q) != 0 {
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sieve[i] *= sieve[q]
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}
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}
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if p*q >= n {
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break
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}
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// sigma_x(p^k) = p^(kx) + sigma_x(p^(k-1))
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sieve[p*q] = pow(p*q, x) + sieve[q]
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}
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}
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/*
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DivisorSieve computes sigma_x(k) for k=1 to n, where sigma_x is the divisor sum function. x sets the power each divisor is raised to.
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*/
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func DivisorsSieve(n uint, x uint, buflen uint) chan uint {
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sieve := make([]uint, n)
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sieve[0] = 0
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for i := uint(1); i < n; i++ {
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sieve[i] = 1
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}
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ch := make(chan uint, buflen)
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go func() {
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defer close(ch)
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for i := uint(0); i < n; i++ {
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if i == 0 || i == 1 || sieve[i] != 1 {
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ch <- sieve[i]
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continue
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}
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sieve[i] = pow(i, x) + 1
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updateMultiples(sieve, x, i, n)
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ch <- sieve[i]
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}
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}()
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return ch
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}
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