A126260 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.

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, 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, 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

Offset: 1

Author

Leroy Quet, Dec 22 2006

Keywords

• nonn
• tabf

Comments

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.

Examples

			Table begins:
1
1,2
1,2,3
1,2,4
1,2,3,4,5
1,2,6
...
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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..12325 (rows 1 <= n <= 300).

Programs

Mathematica

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

Extensions

Extended by Ray Chandler, Dec 24 2006