A376612 Triangle read by rows: T(n,k) is the largest divisor of binomial(n,k) which is less than n, with 2 <= k <= n.

1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 3, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 4, 4, 4, 1, 1, 2, 3, 3, 4, 6, 3, 1, 1, 2, 3, 4, 5, 6, 5, 5, 1, 1, 1, 3, 3, 3, 6, 5, 5, 1, 1, 1, 2, 3, 4, 4, 6, 5, 5, 6, 6, 1, 1, 2, 1, 3, 4, 6, 3, 5, 2, 6, 1, 1, 1, 2, 1, 2, 3, 6, 7, 7, 7, 7, 7, 7, 1

Offset

2,5

Links

Stefano Spezia, Table of n, a(n) for n = 2..5051 (first 100 rows of the triangle)

Example

The triangle begins as:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 1, 1;
  1, 2, 3, 3, 1;
  1, 1, 1, 3, 1, 1;
  1, 2, 2, 4, 4, 4, 1;
  1, 2, 3, 3, 4, 6, 3, 1;
  1, 2, 3, 4, 5, 6, 5, 5, 1;
  1, 1, 3, 3, 3, 6, 5, 5, 1, 1;
  1, 2, 3, 4, 4, 6, 5, 5, 6, 6, 1;
  1, 2, 1, 3, 4, 6, 3, 5, 2, 6, 1, 1;
  ...

Mathematica

T[n_, k_]:=Max[Select[Divisors[Binomial[n, k]], #<k &]]; Table[T[n, k], {n, 2, 14}, {k, 2, n}]//Flatten

Crossrefs

Cf. A000012 (n=k or k=0), A007318, A027750.

Cf. A376611 (less than n).

Sequence in context: A273619 A327522 A034003 * A306722 A168508 A177994

Adjacent sequences: A376609 A376610 A376611 * A376614 A376615 A376616

Keyword

nonn,look,tabl

Author

Stefano Spezia, Sep 29 2024

Status

approved