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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.
2
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
0,13
COMMENTS
For any n > 0, the n-th row has A001651(n) nonzero terms.
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)
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).
EXAMPLE
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
PROG
(PARI) T(n, k) = for (x=1, oo, if (n\x==k\x, return (n\x)))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Jan 31 2020
STATUS
approved