A096006 Triangle read by rows: T(n,k) = largest prime factor of binomial(n,k), 1 <= k <= n-1.

2, 3, 3, 2, 3, 2, 5, 5, 5, 5, 3, 5, 5, 5, 3, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 2, 3, 3, 7, 7, 7, 7, 3, 3, 5, 5, 5, 7, 7, 7, 5, 5, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 3, 11, 11, 11, 11, 11, 11, 11, 11, 11, 3, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 7, 13, 13, 13, 13, 13, 13, 13

Offset

2,1

Links

Andrew Howroyd, Table of n, a(n) for n = 2..1276 (first 50 rows)

Formula

T(n,k) = A006530(A007318(n,k)).

T(n,k) = A098802(n,k).

Example

Triangle begins:
  2;
  3, 3;
  2, 3, 2;
  5, 5, 5, 5;
  3, 5, 5, 5, 3;
  7, 7, 7, 7, 7, 7;
  2, 7, 7, 7, 7, 7, 2;
  3, 3, 7, 7, 7, 7, 3, 3;
  5, 5, 5, 7, 7, 7, 5, 5, 5;
  ...
n Pascal's Triangle
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
so 2,3,2 = largest prime factors of row 4 = entries position 4,5,6 in the sequence.
4' 2 3 2

Prog

(PARI) T(n, k) = { my(f=factor(binomial(n, k))[, 1]); if(!#f, 1, f[#f]) }
{ for(n=2, 10, for(k=1, n-1, print1(T(n, k), ", ")); print) }

Crossrefs

Cf. A006530, A007318, A096007.

Essentially A098802 without first column and last diagonal.

Sequence in context: A218774 A270824 A048198 * A182128 A131294 A276869

Adjacent sequences: A096003 A096004 A096005 * A096007 A096008 A096009

Keyword

nonn,tabl,easy

Author

Cino Hilliard, Jul 25 2004

Extensions

Offset corrected by Andrew Howroyd, Dec 18 2024

Status

approved