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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.

%I A060441 #15 Jul 02 2025 16:02:01
%S A060441 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 A060441 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 A060441 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 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.
%C A060441 Rows have irregular lengths.
%C A060441 T(n,k) = A027746(A000045(n),k), k = 1 .. A038575(n). - _Reinhard Zumkeller_, Aug 30 2014
%H A060441 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas factorizations</a>
%e A060441 Triangle begins:
%e A060441   0;
%e A060441   1;
%e A060441   1;
%e A060441   2;
%e A060441   3;
%e A060441   5;
%e A060441   2, 2, 2;
%e A060441   13;
%e A060441   3, 7;
%e A060441   2, 17;
%e A060441   ...
%p A060441 with(combinat); A060441 := n->ifactor(fibonacci(n));
%p A060441 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 A060441 (Haskell)
%o A060441 a060441 n k = a060441_tabf !! (n-1) !! (k-1)
%o A060441 a060441_row n = a060441_tabf !! (n-1)
%o A060441 a060441_tabf = [0] : [1] : [1] : map a027746_row (drop 3 a000045_list)
%o A060441 -- _Reinhard Zumkeller_, Aug 30 2014
%Y A060441 A000045, A060442.
%Y A060441 Cf. A038575 (row lengths), A027746, A001222.
%K A060441 nonn,tabf,easy
%O A060441 0,4
%A A060441 _N. J. A. Sloane_, Apr 07 2001
%E A060441 More terms from _James Sellers_, Apr 09 2001