%I A125728
%S A125728 1,2,4,5,10,7,18,16,23,19,42,24,58,38,46,56,96,52,120,72,93,93,172,91,
%T A125728 171,132,176,143,270,116,308,218,237,228,280,201,432,286,330,275,530,
%U A125728 237,584,368,394,417,696,357,666,431,570,515,882,452,716,565,712,665
%N A125728 a(n) = sum{k=1 to n}(number of positive integers <=k which are coprime 
               to both k and n).
%C A125728 Equals row sums of triangle A144379 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 19 2008]
%H A125728 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A125728 a(n) = sum{j=1 to n} sum{k|(n*j)} mu(k) * floor(j/k), where mu(k) is 
               the Mobius (Moebius) function and the inner sum is over the positive 
               divisors, k, of (n*j).
%e A125728 The positive integers coprime to k and <= k are, as k runs from 1 to 
               8, 1; 1; 1,
%e A125728 2; 1,3; 1,2,3,4; 1,5; 1,2,3,4,5,6; 1,3,5,7. So we want, so as to
%e A125728 get a(8), the number of 1's, 3's, 5's and 7's in this concatenated
%e A125728 list, since the positive integers <=8 and coprime to 8 are 1,3,5,
%e A125728 7. In the concatenated list there are eight 1's, four 3's, three
%e A125728 5's and one 7. So a(8) = 8+4+3+1 = 16.
%t A125728 f[n_] := Sum[Sum[ Boole[GCD[j, k] == 1 && GCD[j, n] == 1], {j, k}], {k, 
               n}];Table[f[n], {n, 60}] (*Chandler*)
%Y A125728 A144379 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2008]
%Y A125728 Sequence in context: A067298 A077389 A122991 this_sequence A156799 A003278 
               A004792
%Y A125728 Adjacent sequences: A125725 A125726 A125727 this_sequence A125729 A125730 
               A125731
%K A125728 nonn
%O A125728 1,2
%A A125728 Leroy Quet Feb 02 2007
%E A125728 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 03 2007