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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
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
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.)