Decomposing a Factorial into Large Factors

Re:Decomposing a Factorial into Large Factors by btilly on Friday March 28, 2025 @01:32PM (#43508025)

You factor N! into N factors, and look at the smallest of those factors. t(N) is the largest that the smallest factor can be. Here are the best factorizations going slightly beyond the part of https://oeis.org/A034258 that was quoted by Terry Tao.

  1! =  1
  2! =  1 * 2
  3! =  1 * 2 * 3
  4! =  2 * 2 * 2 * 3
  5! =  2 * 2 * 2 * 3 * 5
  6! =  2 * 2 * 3 * 3 * 4 * 5
  7! =  2 * 2 * 3 * 3 * 4 * 5 * 7
  8! =  2 * 3 * 3 * 4 * 4 * 4 * 5 * 7
  9! =  3 * 3 * 3 * 4 * 4 * 4 * 5 * 6 * 7
  10! = 3 * 3 * 4 * 4 * 4 * 5 * 5 * 6 * 6 * 7
  11! = 3 * 3 * 4 * 4 * 4 * 5 * 5 * 6 * 6 * 7 * 11
  12! = 3 * 4 * 4 * 4 * 5 * 5 * 6 * 6 * 6 * 6 *  7 * 11
  13! = 3 * 4 * 4 * 4 * 5 * 5 * 6 * 6 * 6 * 6 *  7 * 11 * 13
  14! = 4 * 4 * 4 * 5 * 5 * 6 * 6 * 6 * 6 * 6 *  7 *  7 * 11 * 13
  15! = 4 * 5 * 5 * 5 * 6 * 6 * 6 * 6 * 6 * 6 *  7 *  7 *  8 * 11 * 13
  16! = 5 * 5 * 5 * 6 * 6 * 6 * 6 * 6 * 6 * 7 *  7 *  8 *  8 *  8 * 11 * 13

[ Parent | on HN ]

Re:Decomposing a Factorial into Large Factors by vintermann on Friday March 28, 2025 @02:15PM (#43508439)

Is the number of factors when you write it out this way, always one more than the previous?

EDIT: Never mind, that's part of the definition of the problem!

[ Parent | on HN ]