A331902 T(n, k) = floor(n/m) where m is the least positive integer such that floor(n/m) = floor(k/m). Square array read by antidiagonals, for n >= 0 and k >= 0.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 4, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 1, 0

Offset: 0

Author

Rémy Sigrist, Jan 31 2020

Keywords

• nonn
• tabl

Comments

For any n > 0, the n-th row has A001651(n) nonzero terms.

Examples

			Array T(n, k) begins (with dots instead of 0's for readability):
   n\k|   0   1   2   3   4   5   6   7   8   9  10  11  12
   ---+----------------------------------------------------
     0|   .   .   .   .   .   .   .   .   .   .   .   .   .
     1|   .   1   .   .   .   .   .   .   .   .   .   .   .
     2|   .   .   2   1   .   .   .   .   .   .   .   .   .
     3|   .   .   1   3   1   1   .   .   .   .   .   .   .
     4|   .   .   .   1   4   2   1   1   .   .   .   .   .
     5|   .   .   .   1   2   5   1   1   1   1   .   .   .
     6|   .   .   .   .   1   1   6   3   2   1   1   1   .
     7|   .   .   .   .   1   1   3   7   2   1   1   1   1
     8|   .   .   .   .   .   1   2   2   8   4   2   2   1
     9|   .   .   .   .   .   1   1   1   4   9   3   3   1
    10|   .   .   .   .   .   .   1   1   2   3  10   5   2
    11|   .   .   .   .   .   .   1   1   2   3   5  11   2
    12|   .   .   .   .   .   .   .   1   1   1   2   2  12
		

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), red pixels correspond to 0's)

Crossrefs

Cf. A001651, A213633, A331886.

Programs

PARI

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

Formula

T(n, k) = floor(n/A331886(n, k)) = floor(k/A331886(n, k)).

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

T(n, k) = 0 iff max(n, k) >= 2*min(n, k).

T(n, n+1) = A213633(n+1).