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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, 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
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 20 2006
EXTENSIONS
Extended by Ray Chandler, Dec 21 2006
STATUS
approved