A060441 Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), with repetition.

0, 1, 1, 2, 3, 5, 2, 2, 2, 13, 3, 7, 2, 17, 5, 11, 89, 2, 2, 2, 2, 3, 3, 233, 13, 29, 2, 5, 61, 3, 7, 47, 1597, 2, 2, 2, 17, 19, 37, 113, 3, 5, 11, 41, 2, 13, 421, 89, 199, 28657, 2, 2, 2, 2, 2, 3, 3, 7, 23, 5, 5, 3001, 233, 521, 2, 17, 53, 109, 3, 13, 29, 281, 514229, 2, 2, 2, 5, 11, 31, 61

Offset: 0

Author

N. J. A. Sloane, Apr 07 2001

Keywords

• nonn
• tabf
• easy

Comments

Rows have irregular lengths.

T(n,k) = A027746(A000045(n),k), k = 1 .. A038575(n). - Reinhard Zumkeller, Aug 30 2014

Examples

			Triangle begins:
  0;
  1;
  1;
  2;
  3;
  5;
  2, 2, 2;
  13;
  3, 7;
  2, 17;
  ...
		

Links

• Blair Kelly, Fibonacci and Lucas factorizations

Crossrefs

A000045, A060442.

Cf. A038575 (row lengths), A027746, A001222.

Programs

Haskell

a060441 n k = a060441_tabf !! (n-1) !! (k-1)
a060441_row n = a060441_tabf !! (n-1)
a060441_tabf = [0] : [1] : [1] : map a027746_row (drop 3 a000045_list)
-- Reinhard Zumkeller, Aug 30 2014

Maple

with(combinat); A060441 := n->ifactor(fibonacci(n));
with(numtheory): with(combinat): for i from 3 to 50 do for j from 1 to nops(ifactors(fibonacci(i))[2]) do for k from 1 to ifactors(fibonacci(i))[2][j][2] do printf(`%d,`, ifactors(fibonacci(i))[2][j][1]) od: od: od:

Extensions

More terms from James Sellers, Apr 09 2001