A123324 Number of integer-sided triangles with all sides <= n and sides relatively prime.

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

Author

Franklin T. Adams-Watters, Sep 25 2006

Keywords

• easy
• nonn

Comments

Number of triples a,b,c with a<=b<=c

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002623, A123323, A123325.

Programs

Mathematica

A123323[n_] := DivisorSum[n, Floor[(#+1)^2/4]*MoebiusMu[n/#]&]; Array[ A123323, 60] // Accumulate (* Jean-François Alcover, Dec 07 2015 *)

PARI

A123323(n)=sum(k=1,n,sumdiv(k,d,floor((d+1)^2/4)*moebius(k/d)));

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)).

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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