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Irregular triangle read by rows where row n contains the positive integers k, k<=n, where every positive integer <=k and coprime to k is also coprime to n.
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%I #13 Oct 10 2019 13:55:16

%S 1,1,2,1,2,3,1,2,4,1,2,3,4,5,1,2,6,1,2,3,4,5,6,7,1,2,4,6,8,1,2,3,6,9,

%T 1,2,4,10,1,2,3,4,5,6,7,8,9,10,11,1,2,6,12,1,2,3,4,5,6,7,8,9,10,11,12,

%U 13,1,2,4,6,14,1,2,3,15,1,2,4,6,8,10,12,14,16,1,2,3,4,5,6,7,8,9,10,11,12

%N Irregular triangle read by rows where row n contains the positive integers k, k<=n, where every positive integer <=k and coprime to k is also coprime to n.

%C The first term of each row is 1. The second term of each row, except for row 1, is 2. The last term of row n is n.

%H Michael De Vlieger, <a href="/A126260/b126260.txt">Table of n, a(n) for n = 1..12325</a> (rows 1 <= n <= 300).

%e Table begins:

%e 1

%e 1,2

%e 1,2,3

%e 1,2,4

%e 1,2,3,4,5

%e 1,2,6

%e ...

%e Row 10 is (1,2,4,10) because the positive integers <=1 and coprime to 1 are {1}, for 2 they are {1}, for 4 they are {1,3}, for 10 they are {1,3,7, 9}; and 1,1,1,3,1,3,7,9 are each coprime to 10.

%t f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Select[Range[n], Times @@ GCD[f[ # ], n] == 1 &];Flatten@Table[g[n], {n, 17}] (* _Ray Chandler_, Dec 24 2006 *)

%t Table[Select[Range@ n, Function[k, AllTrue[Select[Range@ k, CoprimeQ[#, k] &], CoprimeQ[#, n] &]]], {n, 17}] // Flatten (* _Michael De Vlieger_, Aug 21 2017 *)

%K nonn,tabf

%O 1,3

%A _Leroy Quet_, Dec 22 2006

%E Extended by _Ray Chandler_, Dec 24 2006