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A123324
Number of integer-sided triangles with all sides <= n and sides relatively prime.
5
1, 2, 5, 9, 17, 24, 39, 53, 74, 94, 129, 155, 203, 242, 294, 346, 426, 483, 582, 658, 760, 855, 998, 1098, 1258, 1390, 1561, 1711, 1935, 2083, 2338, 2538, 2788, 3012, 3312, 3534, 3894, 4173, 4521, 4817, 5257, 5551, 6034, 6404, 6848, 7255, 7830, 8222, 8831
OFFSET
1,2
COMMENTS
Number of triples a,b,c with a<=b<=c<a+b, gcd(a,b,c)=1 and c<=n.
LINKS
FORMULA
Partial sums of A123323.
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)).
MATHEMATICA
A123323[n_] := DivisorSum[n, Floor[(#+1)^2/4]*MoebiusMu[n/#]&]; Array[ A123323, 60] // Accumulate (* Jean-François Alcover, Dec 07 2015 *)
PROG
(PARI) A123323(n)=sum(k=1, n, sumdiv(k, d, floor((d+1)^2/4)*moebius(k/d)));
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved