login
Triangle read by rows in which row n lists the proper nondivisors of n, or zero if n <= 2.
13

%I #26 Dec 23 2015 02:58:21

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

%C Define "proper nondivisors of n" as the positive numbers less than n that do not divide n.

%C Note that a(1) = 0 and a(2) = 0, by convention.

%C Row sums give A024816.

%C Row products give A055067, except the first two rows. - _Reinhard Zumkeller_, Feb 06 2012

%C T(n,1) = A199968(n). - _Reinhard Zumkeller_, Oct 02 2015

%C The n-th row has A049820(n) terms. - _Michel Marcus_, Dec 23 2015

%H Reinhard Zumkeller, <a href="/A173540/b173540.txt">Rows n=1..150 of triangle, flattened</a>

%e If written as a triangle:

%e 0;

%e 0;

%e 2;

%e 3;

%e 2, 3, 4;

%e 4, 5;

%e 2, 3, 4, 5, 6;

%e 3, 5, 6, 7;

%e 2, 4, 5, 6, 7, 8;

%e 3, 4, 6, 7, 8, 9;

%e 2, 3, 4, 5, 6, 7, 8, 9, 10;

%e 5, 7, 8, 9, 10, 11;

%e 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;

%e 3, 4, 5, 6, 8, 9, 10, 11, 12, 13;

%e 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14;

%e 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15;

%t Join[{0, 0}, Flatten[Table[Complement[Range[n], Divisors[n]], {n, 1, 20}]]] (* _Geoffrey Critzer_, Dec 13 2014 *)

%o (Haskell)

%o a173540 n k = a173540_row n !! (k-1)

%o a173540_row n = a173540_tabf !! (n-1)

%o a173540_tabf = [0] : [0] : map

%o (\v -> [w | w <- [2 .. v - 1], mod v w > 0]) [3..]

%o -- _Reinhard Zumkeller_, Oct 02 2015, Feb 06 2012

%Y Cf. A027750, A049820, A177235.

%Y Cf. A199968, A024816 (row sums).

%K easy,nonn,tabf

%O 1,3

%A _Omar E. Pol_, May 24 2010