A096007 Triangle read by rows: T(n,k) = smallest prime factor of binomial(n,k), 1 <= k <= n-1.

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

Offset

2,1

Links

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

Formula

T(n,k) = A020639(A007318(n,k)).

Example

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

Prog

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

Crossrefs

Cf. A007318, A020639, A096006.

Sequence in context: A011154 A048466 A096838 * A269043 A309952 A059252

Adjacent sequences: A096004 A096005 A096006 * A096008 A096009 A096010

Keyword

nonn,tabl,easy

Author

Cino Hilliard, Jul 25 2004

Extensions

Offset corrected by Andrew Howroyd, Dec 18 2024

Status

approved