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%I #10 Oct 10 2019 13:59:55
%S 1,1,2,4,8,4,12,32,16,12,20,28,44,40,4,228,64,256,292,76,4,72,88,328,
%T 80,52,328,48,116,4,120,2384,4,76,28,496,184,456,28,288,908,4,256,172,
%U 124,284,300,1540,1656,2132,28,2248,428,3196,1572,1684,712,328,428,424,428
%N a(1)=1. a(n) = sum of the earlier terms, a(k) (for 1<=k<=n-1), where every integer coprime to a(k) and <= a(k) is also coprime to n.
%e 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):{1,3}, for a(5):{1,3,5,7}, for a(6):{1,3}, for a(7):{1,5,7,11} and for a(8):{1,3,5,7,...,29,31}.
%e 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 terms a(1)=1,a(2)=1,a(3)=2 and a(7)=12. So a(9) = 1+1+2+12 = 16.
%t f[n_, k_] := Select[Range[k], GCD[ #, n] == 1 &];g[l_List] := Block[{fn = f[Length[l] + 1, Max @@ l]},Append[l, Plus @@ Select[l, Union[f[ #, # ], fn] == fn &]]];Nest[g, {1}, 60] (* _Ray Chandler_, Dec 21 2006 *)
%Y Cf. A126214.
%K nonn
%O 1,3
%A _Leroy Quet_, Dec 20 2006
%E Extended by _Ray Chandler_, Dec 21 2006
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