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

1,2

Comments

Number of triples a,b,c with a<=b<=c<a+b, gcd(a,b,c)=1 and c<=n.

Links

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

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

Cf. A002623, A123323, A123325.

Sequence in context: A348836 A036711 A080740 * A167887 A023603 A334087

Adjacent sequences: A123321 A123322 A123323 * A123325 A123326 A123327

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Sep 25 2006

Status

approved