A290600 Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly.

2, 2, 3, 4, 2, 4, 6, 3, 6, 2, 4, 5, 6, 8, 2, 3, 4, 6, 8, 9, 10, 2, 4, 6, 7, 8, 10, 12, 3, 5, 6, 9, 10, 12, 2, 4, 6, 8, 10, 12, 14, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 3, 6, 7, 9, 12, 14, 15, 18

Offset: 1

Author

Wolfdieter Lang, Aug 30 2017

Keywords

• nonn
• tabf

Comments

The length of row n is A290599(n).

Row n gives the complement of row A038566(A002808(n), k) with respect to [1, 2, ..., A002808(n) - 1].

Examples

			The irregular triangle T(n, k) begins (N(n) = A002808(n)):
  n   N(n) \ k  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...
  1   4         2
  2   6         2  3  4
  3   8         2  4  6
  4   9         3  6
  5   10        2  4  5  6  8
  6   12        2  3  4  6  8  9 10
  7   14        2  4  6  7  8 10 12
  8   15        3  5  6  9 10 12
  9   16        2  4  6  8 10 12 14
  10  18        2  3  4  6  8  9 10 12 14 15 16
  11  20        2  4  5  6  8 10 12 14 15 16 18
  12  21        3  6  7  9 12 14 15 18
  13  22        2  4  6  8 10 11 12 14 16 18 20
  14  24        2  3  4  6  8  9 10 12 14 15 16 18 20 21 22
  15  25        5 10 15 20
  ...
		

Crossrefs

Cf. A002808, A038566, A290599, A290601, A290602.

Programs

Mathematica

Table[With[{c = FixedPoint[n + PrimePi@ # + 1 &, n + PrimePi@ n + 1]}, Select[Range[c - 1], ! CoprimeQ[#, c] &]], {n, 12}] // Flatten (* Michael De Vlieger, Sep 03 2017 *)

Formula

T(n, k) = k-th entry in the list of increasingly sorted numbers of the set {m = 1..A002808(n)-1: gcd(n, m) not equal to 1}.