A249831
A(n,n) = 1, A(n,k) = A(n,k+1)*k / gcd(A(n,k+1),k)^2 if n>k, A(n,k) = A(n,k-1)*k / gcd(A(n,k-1),k)^2 if n=1, k>=1, read by antidiagonals.
1, 2, 1, 6, 1, 2, 6, 3, 2, 6, 30, 12, 1, 6, 6, 5, 60, 4, 3, 6, 30, 35, 10, 20, 1, 12, 30, 5, 280, 70, 30, 5, 4, 60, 5, 35, 2520, 140, 210, 30, 1, 20, 10, 35, 70, 252, 1260, 420, 210, 6, 5, 30, 70, 70, 70, 2772, 126, 420, 420, 42, 1, 30, 210, 35, 70, 7
Offset: 1
Examples
Square array A(n,k) begins: : 1, 2, 6, 6, 30, 5, 35, 280, 2520, 252, ... : 1, 1, 3, 12, 60, 10, 70, 140, 1260, 126, ... : 2, 2, 1, 4, 20, 30, 210, 420, 420, 42, ... : 6, 6, 3, 1, 5, 30, 210, 420, 420, 42, ... : 6, 6, 12, 4, 1, 6, 42, 84, 84, 210, ... : 30, 30, 60, 20, 5, 1, 7, 56, 504, 1260, ... : 5, 5, 10, 30, 30, 6, 1, 8, 72, 180, ... : 35, 35, 70, 210, 210, 42, 7, 1, 9, 90, ... : 70, 70, 35, 105, 420, 84, 56, 8, 1, 10, ... : 70, 70, 35, 105, 420, 84, 504, 72, 9, 1, ...
Links
- Alois P. Heinz, Antidiagonals n = 1..141, flattened
Crossrefs
Programs
-
Maple
A:= proc(n, k) option remember; `if`(k=n, 1, (r-> r*k/igcd(r, k)^2)(A(n, k+`if`(n>k, 1, -1)))) end: seq(seq(A(n, 1+d-n), n=1..d), d=1..14); -
Mathematica
A[n_, k_] := A[n, k] = If[k == n, 1, Function[{r}, r*k/GCD[r, k]^2][A[n, k+If[n>k, 1, -1]]]]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Dec 02 2014, translated from Maple *)