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
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 smallest of these numbers is 12, so a(7) = 12.
Links
- Branden Aldridge and David A. Corneth, Table of n, a(n) for n = 1..10000 (first 500 terms from Branden Aldridge)
Programs
-
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
Extensions
More terms from David W. Wilson, Aug 28 2001