A060441 - OEIS

%I #14 Jan 07 2025 01:59:29

%S 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,

%T 7,47,1597,2,2,2,17,19,37,113,3,5,11,41,2,13,421,89,199,28657,2,2,2,2,

%U 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

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

%C Rows have irregular lengths.

%C T(n,k) = A027746(A000045(n),k), k = 1 .. A038575(n). - _Reinhard Zumkeller_, Aug 30 2014

%H Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas factorizations</a>

%e Triangle begins:

%e   0;

%e   1;

%e   1;

%e   2;

%e   3;

%e   5;

%e   2, 2, 2;

%e   13;

%e   3, 7;

%e   2, 17;

%e   ...

%p with(combinat); A060441 := n->ifactor(fibonacci(n));

%p 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:

%o (Haskell)

%o a060441 n k = a060441_tabf !! (n-1) !! (k-1)

%o a060441_row n = a060441_tabf !! (n-1)

%o a060441_tabf = [0] : [1] : [1] : map a027746_row (drop 3 a000045_list)

%o -- _Reinhard Zumkeller_, Aug 30 2014

%Y A000045, A060442.

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

%K nonn,tabf,easy,changed

%O 0,4

%A _N. J. A. Sloane_, Apr 07 2001

%E More terms from _James A. Sellers_, Apr 09 2001