Data update
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Ingy döt Net
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2196 changed files with 32999 additions and 3075 deletions
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@ -1,78 +1,108 @@
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import java.util.ArrayList;
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import java.util.Collections;
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import java.util.HashMap;
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import java.util.List;
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import java.util.Set;
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import java.util.TreeSet;
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import java.util.stream.Collectors;
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import java.util.stream.IntStream;
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import java.util.Map;
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public final class AchlllesNumbers {
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public class AchillesNumbers {
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public static void main(String[] aArgs) {
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Set<Integer> perfectPowers = perfectPowers(500_000);
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List<Integer> achilles = achilles(1, 250_000, perfectPowers);
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List<Integer> totients = totients(250_000);
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private Map<Integer, Boolean> pps = new HashMap<>();
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System.out.println("First 50 Achilles numbers:");
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for ( int i = 0; i < 50; i++ ) {
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System.out.print(String.format("%4d%s", achilles.get(i), ( ( i + 1 ) % 10 == 0 ) ? "\n" : " "));
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}
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System.out.println();
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System.out.println("First 50 strong Achilles numbers:");
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for ( int i = 0, count = 0; count < 50; i++ ) {
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if ( achilles.contains(totients.get(achilles.get(i))) ) {
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System.out.print(String.format("%6d%s", achilles.get(i), ( ++count % 10 == 0 ) ? "\n" : " "));
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}
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}
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System.out.println();
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System.out.println("Number of Achilles numbers with:");
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for ( int i = 100; i < 1_000_000; i *= 10 ) {
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final int digits = String.valueOf(i).length() - 1;
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System.out.println(" " + digits + " digits: " + achilles(i / 10, i - 1, perfectPowers).size());
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}
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}
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private static List<Integer> achilles(int aFrom, int aTo, Set<Integer> aPerfectPowers) {
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Set<Integer> result = new TreeSet<Integer>();
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final int cubeRoot = (int) Math.cbrt(aTo / 4);
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final int squareRoot = (int) Math.sqrt(aTo / 8);
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for ( int b = 2; b <= cubeRoot; b++ ) {
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final int bCubed = b * b * b;
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for ( int a = 2; a <= squareRoot; a++ ) {
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int achilles = bCubed * a * a;
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if ( achilles >= aTo ) {
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break;
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}
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if ( achilles >= aFrom && ! aPerfectPowers.contains(achilles) ) {
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result.add(achilles);
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}
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}
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}
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return new ArrayList<Integer>(result);
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}
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private static Set<Integer> perfectPowers(int aN) {
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Set<Integer> result = new TreeSet<Integer>();
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for ( int i = 2, root = (int) Math.sqrt(aN); i <= root; i++ ) {
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for ( int perfect = i * i; perfect < aN; perfect *= i ) {
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result.add(perfect);
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}
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}
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return result;
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}
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private static List<Integer> totients(int aN) {
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List<Integer> result = IntStream.rangeClosed(0, aN).boxed().collect(Collectors.toList());;
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for ( int i = 2; i <= aN; i++ ) {
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if ( result.get(i) == i ) {
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result.set(i, i - 1);
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for ( int j = i * 2; j <= aN; j = j + i ) {
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result.set(j, ( result.get(j) / i ) * ( i - 1 ));
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}
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}
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}
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return result;
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}
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public int totient(int n) {
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int tot = n;
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int i = 2;
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while (i * i <= n) {
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if (n % i == 0) {
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while (n % i == 0) {
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n /= i;
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}
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tot -= tot / i;
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}
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if (i == 2) {
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i = 1;
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}
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i += 2;
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}
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if (n > 1) {
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tot -= tot / n;
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}
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return tot;
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}
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public void getPerfectPowers(int maxExp) {
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double upper = Math.pow(10, maxExp);
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for (int i = 2; i <= Math.sqrt(upper); i++) {
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double fi = i;
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double p = fi;
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while (true) {
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p *= fi;
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if (p >= upper) {
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break;
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}
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pps.put((int) p, true);
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}
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}
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}
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public Map<Integer, Boolean> getAchilles(int minExp, int maxExp) {
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double lower = Math.pow(10, minExp);
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double upper = Math.pow(10, maxExp);
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Map<Integer, Boolean> achilles = new HashMap<>();
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for (int b = 1; b <= (int) Math.cbrt(upper); b++) {
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int b3 = b * b * b;
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for (int a = 1; a <= (int) Math.sqrt(upper); a++) {
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int p = b3 * a * a;
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if (p >= (int) upper) {
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break;
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}
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if (p >= (int) lower) {
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if (!pps.containsKey(p)) {
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achilles.put(p, true);
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}
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}
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}
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}
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return achilles;
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}
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public static void main(String[] args) {
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AchillesNumbers an = new AchillesNumbers();
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int maxDigits = 8;
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an.getPerfectPowers(maxDigits);
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Map<Integer, Boolean> achillesSet = an.getAchilles(1, 5);
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List<Integer> achilles = new ArrayList<>(achillesSet.keySet());
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Collections.sort(achilles);
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System.out.println("First 50 Achilles numbers:");
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for (int i = 0; i < 50; i++) {
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System.out.printf("%4d ", achilles.get(i));
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if ((i + 1) % 10 == 0) {
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System.out.println();
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}
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}
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System.out.println("\nFirst 30 strong Achilles numbers:");
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List<Integer> strongAchilles = new ArrayList<>();
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int count = 0;
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for (int n = 0; count < 30; n++) {
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int tot = an.totient(achilles.get(n));
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if (achillesSet.containsKey(tot)) {
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strongAchilles.add(achilles.get(n));
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count++;
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}
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}
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for (int i = 0; i < 30; i++) {
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System.out.printf("%5d ", strongAchilles.get(i));
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if ((i + 1) % 10 == 0) {
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System.out.println();
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}
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}
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System.out.println("\nNumber of Achilles numbers with:");
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for (int d = 2; d <= maxDigits; d++) {
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int ac = an.getAchilles(d - 1, d).size();
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System.out.printf("%2d digits: %d\n", d, ac);
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}
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}
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}
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