%I #13 Sep 04 2017 11:48:27
%S 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,
%T 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,
%U 15,16,18,3,6,7,9,12,14,15,18
%N Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly.
%C The length of row n is A290599(n).
%C Row n gives the complement of row A038566(A002808(n), k) with respect to [1, 2, ..., A002808(n) - 1].
%F 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}.
%e The irregular triangle T(n, k) begins (N(n) = A002808(n)):
%e n N(n) \ k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...
%e 1 4 2
%e 2 6 2 3 4
%e 3 8 2 4 6
%e 4 9 3 6
%e 5 10 2 4 5 6 8
%e 6 12 2 3 4 6 8 9 10
%e 7 14 2 4 6 7 8 10 12
%e 8 15 3 5 6 9 10 12
%e 9 16 2 4 6 8 10 12 14
%e 10 18 2 3 4 6 8 9 10 12 14 15 16
%e 11 20 2 4 5 6 8 10 12 14 15 16 18
%e 12 21 3 6 7 9 12 14 15 18
%e 13 22 2 4 6 8 10 11 12 14 16 18 20
%e 14 24 2 3 4 6 8 9 10 12 14 15 16 18 20 21 22
%e 15 25 5 10 15 20
%e ...
%t 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 *)
%Y Cf. A002808, A038566, A290599, A290601, A290602.
%K nonn,tabf
%O 1,1
%A _Wolfdieter Lang_, Aug 30 2017