A124611 a(n) = sum of the positive integers k, k<=n, where each positive integer <=k and coprime to k is also coprime to n.
1, 3, 6, 7, 15, 9, 28, 21, 21, 17, 66, 21, 91, 27, 21, 73, 153, 39, 190, 37, 33, 53, 276, 63, 85, 69, 138, 55, 435, 33, 496, 273, 54, 107, 50, 129, 703, 129, 72, 107, 861, 51, 946, 97, 96, 179, 1128, 219, 217, 157, 99, 121, 1431, 273, 80, 153, 123, 269, 1770, 93, 1891
Offset: 1
Keywords
Examples
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}.
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.
Programs
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Mathematica
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 *)
Extensions
Extended by Ray Chandler, Dec 20 2006