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A173540 Triangle read by rows in which row n lists the proper nondivisors of n, or zero if n <= 2.

%I A173540 #26 Dec 23 2015 02:58:21
%S A173540 0,0,2,3,2,3,4,4,5,2,3,4,5,6,3,5,6,7,2,4,5,6,7,8,3,4,6,7,8,9,2,3,4,5,
%T A173540 6,7,8,9,10,5,7,8,9,10,11,2,3,4,5,6,7,8,9,10,11,12,3,4,5,6,8,9,10,11,
%U A173540 12,13,2,4,6,7,8,9,10,11,12,13,14,3,5,6,7,9,10,11,12,13,14,15,2,3,4,5,6,7
%N A173540 Triangle read by rows in which row n lists the proper nondivisors of n, or zero if n <= 2.
%C A173540 Define "proper nondivisors of n" as the positive numbers less than n that do not divide n.
%C A173540 Note that a(1) = 0 and a(2) = 0, by convention.
%C A173540 Row sums give A024816.
%C A173540 Row products give A055067, except the first two rows. - _Reinhard Zumkeller_, Feb 06 2012
%C A173540 T(n,1) = A199968(n). - _Reinhard Zumkeller_, Oct 02 2015
%C A173540 The n-th row has A049820(n) terms. - _Michel Marcus_, Dec 23 2015
%H A173540 Reinhard Zumkeller, <a href="/A173540/b173540.txt">Rows n=1..150 of triangle, flattened</a>
%e A173540 If written as a triangle:
%e A173540   0;
%e A173540   0;
%e A173540   2;
%e A173540   3;
%e A173540   2, 3, 4;
%e A173540   4, 5;
%e A173540   2, 3, 4, 5,  6;
%e A173540   3, 5, 6, 7;
%e A173540   2, 4, 5, 6,  7,  8;
%e A173540   3, 4, 6, 7,  8,  9;
%e A173540   2, 3, 4, 5,  6,  7,  8,  9, 10;
%e A173540   5, 7, 8, 9, 10, 11;
%e A173540   2, 3, 4, 5,  6,  7,  8,  9, 10, 11, 12;
%e A173540   3, 4, 5, 6,  8,  9, 10, 11, 12, 13;
%e A173540   2, 4, 6, 7,  8,  9, 10, 11, 12, 13, 14;
%e A173540   3, 5, 6, 7,  9, 10, 11, 12, 13, 14, 15;
%t A173540 Join[{0, 0}, Flatten[Table[Complement[Range[n], Divisors[n]], {n, 1, 20}]]] (* _Geoffrey Critzer_, Dec 13 2014 *)
%o A173540 (Haskell)
%o A173540 a173540 n k = a173540_row n !! (k-1)
%o A173540 a173540_row n = a173540_tabf !! (n-1)
%o A173540 a173540_tabf = [0] : [0] : map
%o A173540                (\v -> [w | w <- [2 .. v - 1], mod v w > 0]) [3..]
%o A173540 -- _Reinhard Zumkeller_, Oct 02 2015, Feb 06 2012
%Y A173540 Cf. A027750, A049820, A177235.
%Y A173540 Cf. A199968, A024816 (row sums).
%K A173540 easy,nonn,tabf
%O A173540 1,3
%A A173540 _Omar E. Pol_, May 24 2010