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 A343825 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. 1
 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, 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, 14, 8, 9, 10, 0, 1, 4, 6, 4, 10, 12, 14, 15, 16, 18, 11, 0, 1, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS For each prime p, the p-th row is a permutation of the nonprime integers. T(n,k) <= A343881(n,k). Conjecture: T(p,k) = A071537(k) for fixed k and sufficiently large prime p. LINKS Table of n, a(n) for n=1..81. EXAMPLE Table begins: n\k | 0 1 2 3 4 5 6 7 8 9 10 ------+-------------------------------------- 1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 2 | 0, 1, 6, 8, 4, 10, 12, 14, 15, 9, 18 3 | 0, 1, 4, 6, 9, 10, 12, 14, 8, 16, 15 4 | 0, 1, 4, 6, 4, 10, 9, 14, 15, 9, 18 5 | 0, 1, 4, 6, 8, 10, 9, 14, 12, 15, 16 6 | 0, 1, 4, 6, 4, 10, 12, 14, 8, 9, 15 7 | 0, 1, 4, 6, 8, 10, 9, 14, 12, 15, 16 8 | 0, 1, 4, 6, 4, 10, 9, 14, 12, 9, 16 Specifically, T(2,3) = 8 because 3 * 6 * 8 = 12^2, T(3,3) = 6 because 3 * 4^2 * 6^2 = 12^3, T(3,5) = 10 because 5 * 6 * 9 * 10^2 = 30^3, T(4,6) = 9 because 6^2 * 8^2 * 9^3 = 36^4, and T(4,9) = 9 because 9^2 = 3^4. CROSSREFS Row n: A001477 (n=1), A006255 (n=2), A277494 (n=3), A328045 (n=4). Cf. A071537. Sequence in context: A021500 A175197 A367795 * A339031 A367270 A365770 Adjacent sequences: A343822 A343823 A343824 * A343826 A343827 A343828 KEYWORD nonn,tabl AUTHOR Peter Kagey, Apr 30 2021 STATUS approved

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Last modified June 18 20:31 EDT 2024. Contains 373486 sequences. (Running on oeis4.)