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 A123323 Number of integer-sided triangles with maximum side n, with sides relatively prime. 7
 1, 1, 3, 4, 8, 7, 15, 14, 21, 20, 35, 26, 48, 39, 52, 52, 80, 57, 99, 76, 102, 95, 143, 100, 160, 132, 171, 150, 224, 148, 255, 200, 250, 224, 300, 222, 360, 279, 348, 296, 440, 294, 483, 370, 444, 407, 575, 392, 609, 460, 592, 516, 728, 495, 740, 588, 738, 644 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Number of triples a,b,c with a <= b <= c < a+b, gcd(a,b,c) = 1 and c = n. Dropping the requirement for side lengths to be relatively prime this sequence becomes A002620 (with a different offset). See the Sep 2006 comment in A002620. - Peter Munn, Jul 26 2017 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Stackexchange, Number of triplets for which gcd(a,b,c)=1 and c=n, Feb 25 2014 FORMULA Moebius transform of b(n) = floor((n+1)^2/4). G.f.: (G(x)+x-x^2)/2, 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)). MAPLE with(numtheory): a:= n-> add(mobius(n/d)*floor((d+1)^2/4), d=divisors(n)): seq(a(n), n=1..60);  # Alois P. Heinz, Oct 23 2013 MATHEMATICA a[n_] := DivisorSum[n, Floor[(#+1)^2/4]*MoebiusMu[n/#]&]; Array[a, 60] (* Jean-François Alcover, Dec 07 2015 *) PROG (PARI) A123323(n)=sumdiv(n, d, floor((d+1)^2/4)*moebius(n/d)). CROSSREFS Cf. A002620, A051493, A054875, A070110, A123324, A123325. Sequence in context: A049826 A310014 A310015 * A034772 A197138 A065309 Adjacent sequences:  A123320 A123321 A123322 * A123324 A123325 A123326 KEYWORD easy,look,nonn AUTHOR Franklin T. Adams-Watters, Sep 25 2006 STATUS approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)