A057340 - OEIS

%I #28 Jun 02 2022 10:26:18

%S 1,2,6,12,12,12,12,24,72,60,60,72,72,72,120,240,240,180,180,360,360,

%T 360,360,720,720,720,720,720,720,720,720,720,720,720,840,2520,2520,

%U 2520,2520,1440,1440,2520,2520,2520,2520,2520,2520,5040,5040,5040,5040

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

%H Branden Aldridge and David A. Corneth, <a href="/A057340/b057340.txt">Table of n, a(n) for n = 1..10000</a> (first 500 terms from Branden Aldridge)

%e 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.

%o (Java)

%o public class SmallestMultCube {

%o     static int low, highestFrequency = 0;

%o     static int[] counters;

%o     public static void main(String[] args) {

%o         int max=500;

%o         counters = new int[max*max*max+1];

%o         for(int outer=1; outer<=max; outer++) {

%o             tally(outer*outer*outer, 1);

%o             for(int middle=outer-1; middle>=1; middle--) {

%o                 tally(outer*outer*middle, 3); tally(outer*middle*middle, 3);

%o                 for(int inner=middle-1; inner>=1; inner--) {

%o                     tally(outer*middle*inner, 6); } }

%o             System.out.println(outer+" "+low); } }

%o     private static void tally(int number, int repeatFactor) {

%o         counters[number] += repeatFactor;

%o         if(counters[number] >= highestFrequency) {

%o             if (counters[number] == highestFrequency)

%o                 if (number < low) low = number;

%o             if (counters[number] > highestFrequency) {

%o                 highestFrequency = counters[number]; low = number; } } } }

%o // _Branden Aldridge_, Apr 15 2022

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

%K nonn

%O 1,2

%A _Neil Fernandez_, Aug 28 2000

%E More terms from _David W. Wilson_, Aug 28 2001