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

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, 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, 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

Offset

1,3

Comments

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

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

Row sums give A024816.

Row products give A055067, except the first two rows. - Reinhard Zumkeller, Feb 06 2012

T(n,1) = A199968(n). - Reinhard Zumkeller, Oct 02 2015

The n-th row has A049820(n) terms. - Michel Marcus, Dec 23 2015

Links

Reinhard Zumkeller, Rows n=1..150 of triangle, flattened

Example

If written as a triangle:
  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,  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, 12, 13;
  2, 4, 6, 7,  8,  9, 10, 11, 12, 13, 14;
  3, 5, 6, 7,  9, 10, 11, 12, 13, 14, 15;

Mathematica

Join[{0, 0}, Flatten[Table[Complement[Range[n], Divisors[n]], {n, 1, 20}]]] (* Geoffrey Critzer, Dec 13 2014 *)

Prog

(Haskell)
a173540 n k = a173540_row n !! (k-1)
a173540_row n = a173540_tabf !! (n-1)
a173540_tabf = [0] : [0] : map
               (\v -> [w | w <- [2 .. v - 1], mod v w > 0]) [3..]
-- Reinhard Zumkeller, Oct 02 2015, Feb 06 2012

Crossrefs

Cf. A027750, A049820, A177235.

Cf. A199968, A024816 (row sums).

Sequence in context: A002372 A035026 A224962 * A336264 A070770 A292599

Adjacent sequences: A173537 A173538 A173539 * A173541 A173542 A173543

Keyword

easy,nonn,tabf

Author

Omar E. Pol, May 24 2010

Status

approved