A331886 T(n, k) is the least positive m such that floor(n/m) = floor(k/m). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.

1, 2, 2, 3, 1, 3, 4, 3, 3, 4, 5, 4, 1, 4, 5, 6, 5, 2, 2, 5, 6, 7, 6, 5, 1, 5, 6, 7, 8, 7, 6, 3, 3, 6, 7, 8, 9, 8, 7, 3, 1, 3, 7, 8, 9, 10, 9, 8, 7, 2, 2, 7, 8, 9, 10, 11, 10, 9, 8, 4, 1, 4, 8, 9, 10, 11, 12, 11, 10, 9, 4, 4, 4, 4, 9, 10, 11, 12, 13, 12, 11, 10

Offset

0,2

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10010 (antidiagonals 0..140)

Rémy Sigrist, Colored representation of T(n, k) for n, k = 0..1000 (where the hue is function of T(n, k))

Rémy Sigrist, Colored representation of floor(n/T(n, k)) for n, k = 0..1000 (where the hue is function of floor(n/T(n, k)), red pixels correspond to 0's)

Formula

T(n, k) = T(k, n).

T(n, k) = 1 iff n = k.

T(n, k) <= 1 + max(n, k) with equality iff max(n, k) >= 2*min(n, k).

T(n, n+1) = A007978(n+1).

Example

Array T(n, k) begins:
   n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
   ---+----------------------------------------------------
     0|   1   2   3   4   5   6   7   8   9  10  11  12  13
     1|   2   1   3   4   5   6   7   8   9  10  11  12  13
     2|   3   3   1   2   5   6   7   8   9  10  11  12  13
     3|   4   4   2   1   3   3   7   8   9  10  11  12  13
     4|   5   5   5   3   1   2   4   4   9  10  11  12  13
     5|   6   6   6   3   2   1   4   4   5   5  11  12  13
     6|   7   7   7   7   4   4   1   2   3   5   6   6  13
     7|   8   8   8   8   4   4   2   1   3   5   6   6   7
     8|   9   9   9   9   9   5   3   3   1   2   4   4   7
     9|  10  10  10  10  10   5   5   5   2   1   3   3   7
    10|  11  11  11  11  11  11   6   6   4   3   1   2   5
    11|  12  12  12  12  12  12   6   6   4   3   2   1   5
    12|  13  13  13  13  13  13  13   7   7   7   5   5   1

Prog

(PARI) T(n, k) = for (m=1, oo, if (n\m==k\m, return (m)))

Crossrefs

Cf. A007978, A331902.

Sequence in context: A113881 A072030 A217029 * A205456 A080045 A191384

Adjacent sequences: A331883 A331884 A331885 * A331887 A331888 A331889

Keyword

nonn,tabl,look

Author

Rémy Sigrist, Jan 30 2020

Status

approved