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

%I A057340 #28 Jun 02 2022 10:26:18
%S A057340 1,2,6,12,12,12,12,24,72,60,60,72,72,72,120,240,240,180,180,360,360,
%T A057340 360,360,720,720,720,720,720,720,720,720,720,720,720,840,2520,2520,
%U A057340 2520,2520,1440,1440,2520,2520,2520,2520,2520,2520,5040,5040,5040,5040
%N A057340 Smallest of the most frequently occurring numbers in 1-to-n multiplication cube.
%H A057340 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 A057340 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 A057340 (Java)
%o A057340 public class SmallestMultCube {
%o A057340     static int low, highestFrequency = 0;
%o A057340     static int[] counters;
%o A057340     public static void main(String[] args) {
%o A057340         int max=500;
%o A057340         counters = new int[max*max*max+1];
%o A057340         for(int outer=1; outer<=max; outer++) {
%o A057340             tally(outer*outer*outer, 1);
%o A057340             for(int middle=outer-1; middle>=1; middle--) {
%o A057340                 tally(outer*outer*middle, 3); tally(outer*middle*middle, 3);
%o A057340                 for(int inner=middle-1; inner>=1; inner--) {
%o A057340                     tally(outer*middle*inner, 6); } }
%o A057340             System.out.println(outer+" "+low); } }
%o A057340     private static void tally(int number, int repeatFactor) {
%o A057340         counters[number] += repeatFactor;
%o A057340         if(counters[number] >= highestFrequency) {
%o A057340             if (counters[number] == highestFrequency)
%o A057340                 if (number < low) low = number;
%o A057340             if (counters[number] > highestFrequency) {
%o A057340                 highestFrequency = counters[number]; low = number; } } } }
%o A057340 // _Branden Aldridge_, Apr 15 2022
%Y A057340 Cf. A025487, A057144, A057338, A057343, A057346.
%K A057340 nonn
%O A057340 1,2
%A A057340 _Neil Fernandez_, Aug 28 2000
%E A057340 More terms from _David W. Wilson_, Aug 28 2001