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Search: id:A123323
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| A123323 |
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Number of integer-sided triangles with maximum side n, with sides relatively prime. |
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+0
4
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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Number of triples a,b,c with a<=b<=c<a+b, gcd(a,b,c)=1, and c=n.
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FORMULA
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Moebius transform of b(n) = floor((n+1)^2/4). G.f. (G(x)+x-x^2)/2, where G(x) = Sum_{k=1}^{infinity} mobius(k)*x^k*(1+2*x^k-x^(2*k))/(1-x^k)^2/(1-x^(2*k)).
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PROGRAM
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(PARI) A123323(n)=sumdiv(n, d, floor((d+1)^2/4)*moebius(n/d)).
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CROSSREFS
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Cf. A002620, A123324, A123325.
Adjacent sequences: A123320 A123321 A123322 this_sequence A123324 A123325 A123326
Sequence in context: A019972 A064406 A049826 this_sequence A034772 A065309 A097689
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 25 2006
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