A057339 Largest of the most frequently occurring numbers in 1-to-n multiplication cube.

1, 4, 6, 12, 20, 24, 24, 48, 72, 120, 120, 120, 120, 168, 120, 240, 240, 360, 360, 360, 360, 360, 360, 720, 720, 720, 720, 1008, 1008, 720, 720, 720, 720, 720, 1680, 2520, 2520, 2520, 2520, 1440, 1440, 2520, 2520, 2520, 2520, 2520, 2520, 5040, 5040, 5040

Offset

1,2

Links

Branden Aldridge, Table of n, a(n) for n = 1..500

Example

M(n) is the array in which m(x,y,z)=x*y*z for x = 1 to n, y = 1 to n and z = 1 to n. In M(7), the most frequently occurring numbers are 12 and 24, each occurring 15 times. The largest of these numbers is 24, so a(7) = 24.

Prog

(Java)
public class LargestMultCube {
    static int high, highestFrequency = 0;
    static int[] counters;
    public static void main(String[] args) {
        int max=500;
        counters = new int[max*max*max+1];
        for(int outer=1; outer<=max; outer++) {
            tally(outer*outer*outer, 1);
            for(int middle=outer-1; middle>=1; middle--) {
                tally(outer*outer*middle, 3); tally(outer*middle*middle, 3);
                for(int inner=middle-1; inner>=1; inner--) {
                    tally(outer*middle*inner, 6); } }
            System.out.println(outer+" "+high); } }
    private static void tally(int number, int repeatFactor) {
        counters[number] += repeatFactor;
        if(counters[number] >= highestFrequency) {
            if (counters[number] == highestFrequency)
                if (number > high) high = number;
            if (counters[number] > highestFrequency) {
                highestFrequency = counters[number]; high = number; } } } }
// Branden Aldridge, Apr 15 2022

Crossrefs

Cf. A057143, A057338, A057342, A057345.

Sequence in context: A063607 A306270 A045956 * A336552 A160856 A019445

Adjacent sequences: A057336 A057337 A057338 * A057340 A057341 A057342

Keyword

nonn

Author

Neil Fernandez, Aug 28 2000

Extensions

More terms from David W. Wilson, Aug 28 2001

Status

approved