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A024362
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Number of primitive Pythagorean triangles with hypotenuse n.
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5
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0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,65
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COMMENTS
| Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, (A, B) = 1, A <= B); sequence gives number of times C takes value n.
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, pp. 116-117, 1966.
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LINKS
| Ron Knott, Pythagorean Triples and Online Calculators
Eric Weisstein's World of Mathematics, Pythagorean Triple
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MATHEMATICA
| Table[a0=IntegerExponent[n, 2]; If[n==1 || a0>0, cnt=0, m=n/2^a0; p=Transpose[FactorInteger[m]][[1]]; c=Count[p, _?(Mod[#, 4]==1 &)]; If[c==Length[p], cnt=2^(c-1), 0]]; cnt, {n, 100}]
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CROSSREFS
| Cf. A024361, A046079, A046080, A020882.
Sequence in context: A073346 A114099 A028613 * A104488 A010103 A086078
Adjacent sequences: A024359 A024360 A024361 * A024363 A024364 A024365
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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