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

1,3

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.

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A366624 A366625 A334428 * A264846 A265691 A334430

Adjacent sequences: A126257 A126258 A126259 * A126261 A126262 A126263

Keyword

nonn,tabf

Author

Leroy Quet, Dec 22 2006

Extensions

Extended by Ray Chandler, Dec 24 2006

Status

approved