A126214 a(1)=1. a(n) = number of earlier terms, a(k) (for 1<=k<=n-1), where every integer coprime to a(k) and <= a(k) is also coprime to n.

1, 1, 2, 3, 4, 3, 6, 5, 6, 4, 10, 5, 12, 7, 5, 9, 16, 6, 18, 6, 9, 10, 22, 9, 12, 13, 15, 9, 28, 3, 30, 18, 14, 15, 11, 12, 36, 18, 17, 8, 40, 7, 42, 13, 9, 21, 46, 16, 21, 9, 21, 15, 52, 16, 13, 12, 26, 26, 58, 4, 60, 29, 14, 37, 14, 7, 66, 23, 29, 6, 70, 20, 72, 34, 11, 27, 20, 12, 78

Offset

1,3

Links

Table of n, a(n) for n=1..79.

Example

The positive integers coprime to a(k) and <= a(k), for 1<=k<=8, are for a(1):{1}, for a(2):{1}, for a(3):{1}, for a(4):{1,2}, for a(5):{1,3}, for a(6):{1,2}, for a(7):{1,5} and for a(8):{1,2,3,4}.
Those terms a(k), 1<=k<=8, which don't have any integers which are not coprime to 9 among those positive integers which are <=a(k) and coprime to a(k) are the six terms a(1)=1,a(2)=1,a(3)=2,a(4)=3,a(6)=3 and a(7)=6. So a(9) = 6.

Mathematica

f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[l_List] := Block[{fn = f[Length[l] + 1]}, Append[l, Length@Select[l, Union[f[ # ], fn] == fn &]]]; Nest[g, {1}, 80] (* Ray Chandler, Dec 21 2006 *)

Crossrefs

Cf. A126215.

Sequence in context: A353201 A229110 A229949 * A126801 A076945 A074792

Adjacent sequences: A126211 A126212 A126213 * A126215 A126216 A126217

Keyword

nonn

Author

Leroy Quet, Dec 20 2006

Extensions

Extended by Ray Chandler, Dec 21 2006

Status

approved