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

1,2

Links

Table of n, a(n) for n=1..61.

Example

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.

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 *)

Crossrefs

Sequence in context: A233757 A341622 A139247 * A281900 A266615 A043305

Adjacent sequences: A124608 A124609 A124610 * A124612 A124613 A124614

Keyword

nonn

Author

Leroy Quet, Dec 20 2006

Extensions

Extended by Ray Chandler, Dec 20 2006

Status

approved