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%I #22 Jun 14 2021 15:56:28
%S 0,0,1,0,1,2,0,1,6,3,0,1,4,8,4,0,1,4,6,4,5,0,1,4,6,9,10,6,0,1,4,6,4,
%T 10,12,7,0,1,4,6,8,10,12,14,8,0,1,4,6,4,10,9,14,15,9,0,1,4,6,8,10,9,
%U 14,8,9,10,0,1,4,6,4,10,12,14,15,16,18,11,0,1,4
%N Table read by antidiagonals upward: T(n,k) is the least m such that there exists a sequence k = b_1 <= b_2 <= ... <= b_t = m such that no term appears n or more times and the product of the sequence is of the form c^n, where c is an integer; n >= 1 and k >= 0.
%C For each prime p, the p-th row is a permutation of the nonprime integers.
%C T(n,k) <= A343881(n,k).
%C Conjecture: T(p,k) = A071537(k) for fixed k and sufficiently large prime p.
%e Table begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 10
%e ------+--------------------------------------
%e 1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
%e 2 | 0, 1, 6, 8, 4, 10, 12, 14, 15, 9, 18
%e 3 | 0, 1, 4, 6, 9, 10, 12, 14, 8, 16, 15
%e 4 | 0, 1, 4, 6, 4, 10, 9, 14, 15, 9, 18
%e 5 | 0, 1, 4, 6, 8, 10, 9, 14, 12, 15, 16
%e 6 | 0, 1, 4, 6, 4, 10, 12, 14, 8, 9, 15
%e 7 | 0, 1, 4, 6, 8, 10, 9, 14, 12, 15, 16
%e 8 | 0, 1, 4, 6, 4, 10, 9, 14, 12, 9, 16
%e Specifically,
%e T(2,3) = 8 because 3 * 6 * 8 = 12^2,
%e T(3,3) = 6 because 3 * 4^2 * 6^2 = 12^3,
%e T(3,5) = 10 because 5 * 6 * 9 * 10^2 = 30^3,
%e T(4,6) = 9 because 6^2 * 8^2 * 9^3 = 36^4, and
%e T(4,9) = 9 because 9^2 = 3^4.
%Y Row n: A001477 (n=1), A006255 (n=2), A277494 (n=3), A328045 (n=4).
%Y Cf. A071537.
%K nonn,tabl
%O 1,6
%A _Peter Kagey_, Apr 30 2021
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