|
%I #10 Oct 11 2019 11:01:31
%S 1,3,6,7,15,9,28,21,21,17,66,21,91,27,21,73,153,39,190,37,33,53,276,
%T 63,85,69,138,55,435,33,496,273,54,107,50,129,703,129,72,107,861,51,
%U 946,97,96,179,1128,219,217,157,99,121,1431,273,80,153,123,269,1770,93,1891
%N a(n) = sum of the positive integers k, k<=n, where each positive integer <=k and coprime to k is also coprime to n.
%e The positive integers coprime to k and <= k, for 1<=k<=8, are for 1:{1}, for 2:{1}, for 3:{1,2}, for 4:{1,3}, for 5:{1,2,3,4}, for 6:{1,5}, for 7:{1, 2,3,4,5,6} and for 8:{1,3,5,7}.
%e Those positive integers k which don't have any integers which are not coprime to 8 among those positive integers which are <=k and coprime to k are 1,2,4,6,8. So a(8) = 1+2+4+6+8 = 21.
%t f[n_] := Select[Range[n], GCD[ #, n] == 1 &];g[n_] := Block[{fn = f[n]},Sum[k*Boole[Union[f[k], fn] == fn], {k, n}]];Table[g[n], {n, 61}] (* _Ray Chandler_, Dec 20 2006 *)
%K nonn
%O 1,2
%A _Leroy Quet_, Dec 20 2006
%E Extended by _Ray Chandler_, Dec 20 2006
|
