

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



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
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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



