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A060442 Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), without repetition.

%I A060442 #31 Jul 02 2025 16:02:01
%S A060442 0,1,1,2,3,5,2,13,3,7,2,17,5,11,89,2,3,233,13,29,2,5,61,3,7,47,1597,2,
%T A060442 17,19,37,113,3,5,11,41,2,13,421,89,199,28657,2,3,7,23,5,3001,233,521,
%U A060442 2,17,53,109,3,13,29,281,514229,2,5,11,31,61,557,2417,3,7,47,2207,2,89
%N A060442 Triangle T(n,k), n >= 0, in which n-th row (for n >= 3) lists prime factors of Fibonacci(n) (see A000045), without repetition.
%C A060442 Rows have irregular lengths.
%C A060442 T(n,k) = A027748(A000045(n),k), k = 1 .. A022307(n). - _Reinhard Zumkeller_, Aug 30 2014
%H A060442 T. D. Noe and Charles R Greathouse IV, <a href="/A060442/b060442.txt">Rows n=0..1422 of triangle, flattened</a> (rows up to 1000 from Noe; using existing factorization databases)
%H A060442 J. Brillhart, P. L. Montgomery and R. D. Silverman, <a href="https://doi.org/10.1090/S0025-5718-1988-0917832-6">Tables of Fibonacci and Lucas factorizations</a>, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
%H A060442 Blair Kelly, <a href="http://mersennus.net/fibonacci//">Fibonacci and Lucas Factorizations</a>
%e A060442 Triangle begins:
%e A060442      0;
%e A060442      1;
%e A060442      1;
%e A060442      2;
%e A060442      3;
%e A060442      5;
%e A060442      2;
%e A060442     13;
%e A060442      3,   7;
%e A060442      2,  17;
%e A060442      5,  11;
%e A060442     89;
%e A060442      2,   3;
%e A060442    233;
%e A060442     13,  29;
%e A060442      2,   5, 61;
%e A060442      3,   7, 47;
%e A060442   1597;
%e A060442      2,  17, 19;
%e A060442     37, 113;
%e A060442      3,   5, 11, 41;
%e A060442    ...
%p A060442 with(numtheory): with(combinat): for i from 3 to 50 do for j from 1 to nops(ifactors(fibonacci(i))[2]) do printf(`%d,`, ifactors(fibonacci(i))[2][j][1]) od: od:
%o A060442 (Haskell)
%o A060442 a060442 n k = a060442_tabf !! n !! k
%o A060442 a060442_row n = a060442_tabf !! n
%o A060442 a060442_tabf = [0] : [1] : [1] : map a027748_row (drop 3 a000045_list)
%o A060442 -- _Reinhard Zumkeller_, Aug 30 2014
%Y A060442 Cf. A000045, A060441.
%Y A060442 Cf. A027748, A022307 (row lengths for n>2), A001221.
%K A060442 nonn,tabf,easy
%O A060442 0,4
%A A060442 _N. J. A. Sloane_, Apr 07 2001
%E A060442 More terms from _James Sellers_, Apr 09 2001