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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.

%I A343881 #16 Jun 14 2021 15:56:37
%S A343881 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 A343881 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 A343881 40,4,4,9,8,20,36,28,16,12,80,44,8192,4,9,8,25,24,49
%N 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.
%C A343881 For prime p, the p-th row consists of distinct integers.
%C A343881 Conjecture: T(p,k) = A064549(k) for fixed k > 1 and sufficiently large p.
%F A343881 T(n,1) = 2^A020639(n).
%e A343881 Table begins:
%e A343881   n\k|    1  2   3   4   5   6   7   8   9   10
%e A343881 -----+-----------------------------------------
%e A343881    2 |    4, 8, 12,  9, 20, 24, 28, 18, 16,  40
%e A343881    3 |    8, 4,  9, 16, 25, 36, 49, 27, 24,  80
%e A343881    4 |    4, 4,  9,  8, 20, 24, 28, 18, 12,  40
%e A343881    5 |   32, 4,  9,  8, 25, 36, 49, 16, 27, 100
%e A343881    6 |    4, 4,  9,  8, 20, 24, 28,  9, 16,  40
%e A343881    7 |  128, 4,  9,  8, 25, 36, 49, 16, 27, 100
%e A343881    8 |    4, 4,  9,  8, 20, 24, 28, 16, 12,  40
%e A343881    9 |    8, 4,  9,  8, 25, 36, 49, 16, 24,  80
%e A343881   10 |    4, 4,  9,  8, 20, 24, 28, 16, 16,  40
%e A343881   11 | 2048, 4,  9,  8, 25, 36, 49, 16, 27, 100
%e A343881 T(2, 3) = 12 with  3   * 12   =  6^2.
%e A343881 T(3,10) = 80 with 10^2 * 80   = 20^3.
%e A343881 T(4, 5) = 20 with  5^2 * 20^2 = 10^4.
%e A343881 T(5, 1) = 32 with  1   * 32   =  2^5.
%e A343881 T(6, 8) =  9 with  8^2 *  9^3 =  6^6.
%Y A343881 Rows: A072905 (n=2), A277781 (n=3).
%Y A343881 Cf. A064549, A343825.
%K A343881 nonn,tabl
%O A343881 2,1
%A A343881 _Peter Kagey_, May 02 2021