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%I A123324 #14 Dec 11 2017 02:34:10
%S A123324 1,2,5,9,17,24,39,53,74,94,129,155,203,242,294,346,426,483,582,658,
%T A123324 760,855,998,1098,1258,1390,1561,1711,1935,2083,2338,2538,2788,3012,
%U A123324 3312,3534,3894,4173,4521,4817,5257,5551,6034,6404,6848,7255,7830,8222,8831
%N A123324 Number of integer-sided triangles with all sides <= n and sides relatively prime.
%C A123324 Number of triples a,b,c with a<=b<=c<a+b, gcd(a,b,c)=1 and c<=n.
%H A123324 G. C. Greubel, <a href="/A123324/b123324.txt">Table of n, a(n) for n = 1..10000</a>
%F A123324 Partial sums of A123323.
%F A123324 G.f.: (G(x)+x-x^2)/(2(1-x)), where G(x) = Sum_{k >= 1} mobius(k)*x^k*(1+2*x^k-x^(2*k))/(1-x^k)^2/(1-x^(2*k)).
%t A123324 A123323[n_] := DivisorSum[n, Floor[(#+1)^2/4]*MoebiusMu[n/#]&]; Array[ A123323, 60] // Accumulate (* _Jean-François Alcover_, Dec 07 2015 *)
%o A123324 (PARI) A123323(n)=sum(k=1,n,sumdiv(k,d,floor((d+1)^2/4)*moebius(k/d)));
%Y A123324 Cf. A002623, A123323, A123325.
%K A123324 easy,nonn
%O A123324 1,2
%A A123324 _Franklin T. Adams-Watters_, Sep 25 2006

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