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

Author

Neil Fernandez, Aug 28 2000

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A057143, A057338, A057342, A057345.

Programs

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

Extensions

More terms from David W. Wilson, Aug 28 2001