A343881 Table read by antidiagonals upward: T(n,k) is the least integer m > k such that k^x * m^y = c^n for some positive integers c, x, and y where x < n and y < n; n >= 2, k >= 1.
4, 8, 8, 4, 4, 12, 32, 4, 9, 9, 4, 4, 9, 16, 20, 128, 4, 9, 8, 25, 24, 4, 4, 9, 8, 20, 36, 28, 8, 4, 9, 8, 25, 24, 49, 18, 4, 4, 9, 8, 20, 36, 28, 27, 16, 2048, 4, 9, 8, 25, 24, 49, 18, 24, 40, 4, 4, 9, 8, 20, 36, 28, 16, 12, 80, 44, 8192, 4, 9, 8, 25, 24, 49
Offset: 2
Examples
Table begins: n\k| 1 2 3 4 5 6 7 8 9 10 -----+----------------------------------------- 2 | 4, 8, 12, 9, 20, 24, 28, 18, 16, 40 3 | 8, 4, 9, 16, 25, 36, 49, 27, 24, 80 4 | 4, 4, 9, 8, 20, 24, 28, 18, 12, 40 5 | 32, 4, 9, 8, 25, 36, 49, 16, 27, 100 6 | 4, 4, 9, 8, 20, 24, 28, 9, 16, 40 7 | 128, 4, 9, 8, 25, 36, 49, 16, 27, 100 8 | 4, 4, 9, 8, 20, 24, 28, 16, 12, 40 9 | 8, 4, 9, 8, 25, 36, 49, 16, 24, 80 10 | 4, 4, 9, 8, 20, 24, 28, 16, 16, 40 11 | 2048, 4, 9, 8, 25, 36, 49, 16, 27, 100 T(2, 3) = 12 with 3 * 12 = 6^2. T(3,10) = 80 with 10^2 * 80 = 20^3. T(4, 5) = 20 with 5^2 * 20^2 = 10^4. T(5, 1) = 32 with 1 * 32 = 2^5. T(6, 8) = 9 with 8^2 * 9^3 = 6^6.
Formula
T(n,1) = 2^A020639(n).
Comments