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A078644
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a(n) = tau(2*n^2)/2.
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2
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1, 2, 3, 3, 3, 6, 3, 4, 5, 6, 3, 9, 3, 6, 9, 5, 3, 10, 3, 9, 9, 6, 3, 12, 5, 6, 7, 9, 3, 18, 3, 6, 9, 6, 9, 15, 3, 6, 9, 12, 3, 18, 3, 9, 15, 6, 3, 15, 5, 10, 9, 9, 3, 14, 9, 12, 9, 6, 3, 27, 3, 6, 15, 7, 9, 18, 3, 9, 9, 18, 3, 20, 3, 6, 15, 9, 9, 18, 3, 15, 9, 6, 3, 27, 9, 6, 9, 12, 3, 30, 9, 9, 9, 6, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Inverse Moebius transform of A068068. Number of elements in the set {(x,y): x is odd, x|n, y|n, gcd(x,y)=1}.
The number of Pythagorean points (x,y), 0<x<y, located on the hyperbola y=2n(x-n)/(x-2n) and having "excess" x+y-z = 2n. - Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Jun 07 2005
a(n) is the number of Pythagorean triangles with radius of the inscribed circle equal to n. - Ant King, mathstutoring(AT)ntlworld.com, Mar 06 2006. For number of primitive Pythagorean triangles having inradius n, see A068068(n).
Dirichlet convolution of A048691 and A154269. - R. J. Mathar, Jun 01 2011
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LINKS
| S. Mustonen, Visualization and characterization of Pythagorean triples
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FORMULA
| Multiplicative with a(2^e) = e+1, a(p^e) = 2*e+1, p>2. a(n) = tau(n^2) if n is odd, a(n) = tau(n^2)-a(n/2) if n is even.
Dirichlet g.f. zeta^3(s)/(zeta(2s)*(1+1/2^s)). - R. J. Mathar, Jun 01 2011
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CROSSREFS
| Cf. A000005, A048691.
Sequence in context: A119688 A126868 A134187 * A133700 A087688 A126854
Adjacent sequences: A078641 A078642 A078643 * A078645 A078646 A078647
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KEYWORD
| mult,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 13 2002
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