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