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%I #16 Jun 14 2021 15:56:37
%S 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,
%T 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,
%U 40,4,4,9,8,20,36,28,16,12,80,44,8192,4,9,8,25,24,49
%N 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.
%C For prime p, the p-th row consists of distinct integers.
%C Conjecture: T(p,k) = A064549(k) for fixed k > 1 and sufficiently large p.
%F T(n,1) = 2^A020639(n).
%e Table begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10
%e -----+-----------------------------------------
%e 2 | 4, 8, 12, 9, 20, 24, 28, 18, 16, 40
%e 3 | 8, 4, 9, 16, 25, 36, 49, 27, 24, 80
%e 4 | 4, 4, 9, 8, 20, 24, 28, 18, 12, 40
%e 5 | 32, 4, 9, 8, 25, 36, 49, 16, 27, 100
%e 6 | 4, 4, 9, 8, 20, 24, 28, 9, 16, 40
%e 7 | 128, 4, 9, 8, 25, 36, 49, 16, 27, 100
%e 8 | 4, 4, 9, 8, 20, 24, 28, 16, 12, 40
%e 9 | 8, 4, 9, 8, 25, 36, 49, 16, 24, 80
%e 10 | 4, 4, 9, 8, 20, 24, 28, 16, 16, 40
%e 11 | 2048, 4, 9, 8, 25, 36, 49, 16, 27, 100
%e T(2, 3) = 12 with 3 * 12 = 6^2.
%e T(3,10) = 80 with 10^2 * 80 = 20^3.
%e T(4, 5) = 20 with 5^2 * 20^2 = 10^4.
%e T(5, 1) = 32 with 1 * 32 = 2^5.
%e T(6, 8) = 9 with 8^2 * 9^3 = 6^6.
%Y Rows: A072905 (n=2), A277781 (n=3).
%Y Cf. A064549, A343825.
%K nonn,tabl
%O 2,1
%A _Peter Kagey_, May 02 2021