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 g

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 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