A057340 Smallest of the most frequently occurring numbers in 1-to-n multiplication cube.

1, 2, 6, 12, 12, 12, 12, 24, 72, 60, 60, 72, 72, 72, 120, 240, 240, 180, 180, 360, 360, 360, 360, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 840, 2520, 2520, 2520, 2520, 1440, 1440, 2520, 2520, 2520, 2520, 2520, 2520, 5040, 5040, 5040, 5040

Offset

1,2

Links

Branden Aldridge and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 500 terms from Branden Aldridge)

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 smallest of these numbers is 12, so a(7) = 12.

Prog

(Java)
public class SmallestMultCube {
    static int low, 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+" "+low); } }
    private static void tally(int number, int repeatFactor) {
        counters[number] += repeatFactor;
        if(counters[number] >= highestFrequency) {
            if (counters[number] == highestFrequency)
                if (number < low) low = number;
            if (counters[number] > highestFrequency) {
                highestFrequency = counters[number]; low = number; } } } }
// Branden Aldridge, Apr 15 2022

Crossrefs

Cf. A025487, A057144, A057338, A057343, A057346.

Sequence in context: A130503 A278232 A074385 * A092427 A058198 A096075

Adjacent sequences: A057337 A057338 A057339 * A057341 A057342 A057343

Keyword

nonn

Author

Neil Fernandez, Aug 28 2000

Extensions

More terms from David W. Wilson, Aug 28 2001

Status

approved