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Achilles numbers: Difference between revisions

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Achilles numbers (view source)

Revision as of 01:48, 23 January 2024

417 bytes added ,  4 months ago
→‎{{header|Java}}: update java code, correct result of "Number of Achilles numbers with" from up to 5 digits to up to 8 digits
(→‎{{header|C#}}: fix typo)
(→‎{{header|Java}}: update java code, correct result of "Number of Achilles numbers with" from up to 5 digits to up to 8 digits)
Line 2,392:
=={{header|Java}}==
<syntaxhighlight lang="java">
 
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.SetMap;
import java.util.TreeSet;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
 
public final class AchlllesNumbersAchillesNumbers {
 
private Map<Integer, Boolean> pps = new HashMap<>();
public static void main(String[] aArgs) {
Set<Integer> perfectPowers = perfectPowers(500_000);
List<Integer> achilles = achilles(1, 250_000, perfectPowers);
List<Integer> totients = totients(250_000);
 
public int totient(int n) {
System.out.println("First 50 Achilles numbers:");
for ( int itot = 0n; i < 50; i++ ) {
int i = 2;
System.out.print(String.format("%4d%s", achilles.get(i), ( ( i + 1 ) % 10 == 0 ) ? "\n" : " "));
while (i * i <= n) {
}
if (n % i == 0) {
System.out.println();
while (n % i == 0) {
n /= i;
System.out.println("First 50 strong Achilles numbers:");
for ( int i = 0, count = 0; count < 50; i++ ) {}
tot -= tot / i;
if ( achilles.contains(totients.get(achilles.get(i))) ) {
}
System.out.print(String.format("%6d%s", achilles.get(i), ( ++count % 10 == 0 ) ? "\n" : " "));
if (i == 2) {
}
i = 1;
}
}
System.out.println();
i += 2;
}
System.out.println("Number of Achilles numbers with:");
for ( int i =if 100; i < 1_000_000; i *=(n 10> 1) {
tot -= tot / n;
final int digits = String.valueOf(i).length() - 1;
}
System.out.println(" " + digits + " digits: " + achilles(i / 10, i - 1, perfectPowers).size());
return tot;
}
}
}
private static List<Integer> achilles(int aFrom, int aTo, Set<Integer> aPerfectPowers) {
Set<Integer> result = new TreeSet<Integer>();
final int cubeRoot = (int) Math.cbrt(aTo / 4);
final int squareRoot = (int) Math.sqrt(aTo / 8);
for ( int b = 2; b <= cubeRoot; b++ ) {
final int bCubed = b * b * b;
for ( int a = 2; a <= squareRoot; a++ ) {
int achilles = bCubed * a * a;
if ( achilles >= aTo ) {
break;
}
if ( achilles >= aFrom && ! aPerfectPowers.contains(achilles) ) {
result.add(achilles);
}
}
}
return new ArrayList<Integer>(result);
}
private static Set<Integer> perfectPowers(int aN) {
Set<Integer> result = new TreeSet<Integer>();
for ( int i = 2, root = (int) Math.sqrt(aN); i <= root; i++ ) {
for ( int perfect = i * i; perfect < aN; perfect *= i ) {
result.add(perfect);
}
}
return result;
}
private static List<Integer> totients(int aN) {
List<Integer> result = IntStream.rangeClosed(0, aN).boxed().collect(Collectors.toList());;
for ( int i = 2; i <= aN; i++ ) {
if ( result.get(i) == i ) {
result.set(i, i - 1);
for ( int j = i * 2; j <= aN; j = j + i ) {
result.set(j, ( result.get(j) / i ) * ( i - 1 ));
}
}
}
return result;
}
 
public void getPerfectPowers(int maxExp) {
double upper = Math.pow(10, maxExp);
for (int i = 2; i <= Math.sqrt(upper); i++) {
double fi = i;
double p = fi;
while (true) {
p *= fi;
if (p >= upper) {
break;
}
pps.put((int) p, true);
}
}
}
 
public Map<Integer, Boolean> getAchilles(int minExp, int maxExp) {
double lower = Math.pow(10, minExp);
double upper = Math.pow(10, maxExp);
Map<Integer, Boolean> achilles = new HashMap<>();
for (int b = 1; b <= (int) Math.cbrt(upper); b++) {
int b3 = b * b * b;
for (int a = 1; a <= (int) Math.sqrt(upper); a++) {
int p = b3 * a * a;
if (p >= (int) upper) {
break;
}
if (p >= (int) lower) {
if (!pps.containsKey(p)) {
achilles.put(p, true);
}
}
}
}
return achilles;
}
 
public static void main(String[] args) {
AchillesNumbers an = new AchillesNumbers();
 
int maxDigits = 8;
an.getPerfectPowers(maxDigits);
Map<Integer, Boolean> achillesSet = an.getAchilles(1, 5);
List<Integer> achilles = new ArrayList<>(achillesSet.keySet());
Collections.sort(achilles);
 
System.out.println("First 50 Achilles numbers:");
for (int i = 0; i < 50; i++) {
System.out.printf("%4d ", achilles.get(i));
if ((i + 1) % 10 == 0) {
System.out.println();
}
}
 
System.out.println("\nFirst 30 strong Achilles numbers:");
List<Integer> strongAchilles = new ArrayList<>();
int count = 0;
for (int n = 0; count < 30; n++) {
int tot = an.totient(achilles.get(n));
if (achillesSet.containsKey(tot)) {
strongAchilles.add(achilles.get(n));
count++;
}
}
for (int i = 0; i < 30; i++) {
System.out.printf("%5d ", strongAchilles.get(i));
if ((i + 1) % 10 == 0) {
System.out.println();
}
}
 
System.out.println("\nNumber of Achilles numbers with:");
for (int d = 2; d <= maxDigits; d++) {
int ac = an.getAchilles(d - 1, d).size();
System.out.printf("%2d digits: %d\n", d, ac);
}
}
}
</syntaxhighlight>
Line 2,475 ⟶ 2,504:
<pre>
First 50 Achilles numbers:
72 108 200 288 392 432 500 648 675 800
864 968 972 1125 1152 1323 1352 1372 1568 1800
1944 2000 2312 2592 2700 2888 3087 3200 3267 3456
3528 3872 3888 4000 4232 4500 4563 4608 5000 5292
5324 5400 5408 5488 6075 6125 6272 6728 6912 7200
 
First 5030 strong Achilles numbers:
500 864 1944 2000 2592 3456 5000 10125 10368 12348
12500 16875 19652 19773 30375 31104 32000 33275 37044 40500
49392 50000 52488 55296 61731 64827 67500 69984 78608 80000
81000 83349 84375 93312 108000 111132 124416 128000 135000 148176
151875 158184 162000 165888 172872 177957 197568 200000 202612 209952
 
Number of Achilles numbers with:
2 digits: 1
3 digits: 12
4 digits: 47
5 digits: 192
6 digits: 664
7 digits: 2242
8 digits: 7395
 
</pre>
 
Aspen138
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