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Search: id:A143714
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| A143714 |
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Number of pairs (a,b), 1 <= a <= b <= n, such that (a+b)^2+n^2 is a square. |
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3
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| 0, 0, 2, 1, 0, 3, 0, 4, 4, 0, 0, 11, 0, 0, 10, 8, 0, 7, 0, 17, 18, 0, 0, 28, 0, 0, 10, 16, 0, 19, 0, 15, 18, 0, 6, 33, 0, 0, 14, 42, 0, 35, 0, 16, 42, 0, 0, 77, 0, 0, 18, 19, 0, 19, 24, 53, 20, 0, 0, 120, 0, 0, 60, 29, 30, 34, 0, 25, 24, 12, 0, 114, 0, 0, 46, 28, 18, 27, 0, 103, 28, 0, 0, 140
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Also: Number of cuboids of maximal side length n having integral shortest path going on the surface from one vertex to the opposite one.
Also: Number of subsets {a,b} of {1,..,n} such that (a+b,n) form the shorter two legs of a pythagorean triple.
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LINKS
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Project Euler: Problem 86
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EXAMPLE
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For n=3, we have the 3 x 3 x 1 and the 3 x 2 x 2 cuboid, for which the shortest path on the surface from one vertex to the opposite is of integral length sqrt(3^2 + (2+2)^2) = sqrt(3^2 + (3+1)^2) = 5.
For n=4, there is the 4 x 2 x 1 cuboid having this property.
For n=1,2 and 5 there is no cuboid having this property, i.e. no s >= 2, s <= 2n such that s^2+n^2 would be a square.
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PROGRAM
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(PARI) A143714(M)=sum(a=1, M, sum(b=a, M, issquare((a+b)^2+M^2)))
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CROSSREFS
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Cf. A143715 (partial sums).
Sequence in context: A098493 A058560 A131047 this_sequence A004172 A082754 A063173
Adjacent sequences: A143711 A143712 A143713 this_sequence A143715 A143716 A143717
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Aug 29 2008
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