Duffinian numbers: Difference between revisions
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6399 6400 6401
8449 8450 8451</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.Arrays;
public final class DuffianNumbers {
public static void main(String[] aArgs) {
int[] duffians = createDuffians(11_000);
System.out.println("The first 50 Duffinian numbers:");
int count = 0;
int n = 1;
while ( count < 50 ) {
if ( duffians[n] > 0 ) {
System.out.print(String.format("%4d%s", n, ( ++count % 25 == 0 ? "\n" : "" )));
}
n += 1;
}
System.out.println();
System.out.println("The first 16 Duffinian triplets:");
count = 0;
n = 3;
while( count < 16 ) {
if ( duffians[n - 2] > 0 && duffians[n - 1] > 0 && duffians[n] > 0 ) {
System.out.print(String.format("%22s%s",
"(" + ( n - 2 ) + ", " + ( n - 1 ) + ", " + n + ")", ( ++count % 4 == 0 ? "\n" : "" )));
}
n += 1;
}
System.out.println();
}
private static int[] createDuffians(int aLimit) {
// Create a list where list[i] is the divisor sum of i.
int[] result = new int[aLimit];
Arrays.fill(result, 1);
for ( int i = 2; i < aLimit; i++ ) {
for ( int j = i; j < aLimit; j += i ) {
result[j] += i;
}
}
// Set the divisor sums of non-Duffinian numbers to 0.
result[1] = 0; // 1 is not a Duffinian number.
for ( int n = 2; n < aLimit; n++ ) {
int resultN = result[n];
if ( resultN == n + 1 || gcd(n, resultN) != 1 ) {
// n is prime, or it is not relatively prime to its divisor sum.
result[n] = 0;
}
}
return result;
}
private static int gcd(int aOne, int aTwo) {
if ( aTwo == 0 ) {
return aOne;
}
return gcd(aTwo, aOne % aTwo);
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first 50 Duffinian numbers:
4 8 9 16 21 25 27 32 35 36 39 49 50 55 57 63 64 65 75 77 81 85 93 98 100
111 115 119 121 125 128 129 133 143 144 155 161 169 171 175 183 185 187 189 201 203 205 209 215 217
The first 16 Duffinian triplets:
(63, 64, 65) (323, 324, 325) (511, 512, 513) (721, 722, 723)
(899, 900, 901) (1443, 1444, 1445) (2303, 2304, 2305) (2449, 2450, 2451)
(3599, 3600, 3601) (3871, 3872, 3873) (5183, 5184, 5185) (5617, 5618, 5619)
(6049, 6050, 6051) (6399, 6400, 6401) (8449, 8450, 8451) (10081, 10082, 10083)
</pre>
=={{header|jq}}==
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