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
Keywords
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
Programs
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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