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A094958
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Numbers of the form 2^n or 5*2^n.
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9
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1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 8192, 10240, 16384, 20480, 32768, 40960, 65536, 81920, 131072, 163840, 262144, 327680, 524288, 655360, 1048576, 1310720, 2097152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The subset {a(1),...,a(2k)} together with a(2k+2) is the set of proper divisors of 5*2^k.
For a(n)>4: number of vertices of complete graphs that can be properly edge-colored in such a way that the edges can be partitioned into edge disjoint multicolored isomorphic spanning trees.
(Editor's note: The following 3 comments are equivalent.)
Comment from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 10 2005: This appears to be the same sequence as "Numbers n such that n^2 is not the sum of three nonzero squares". Don Reble and Paul Pollack respond: Yes, that is correct.
Also numbers k such that k^2=a^2+b^2+c^2 has no solutions in the positive integers a, b and c. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Apr 20 2005
The only natural numbers which cannot be the lengths of an interior diagonal of a cuboid with natural edges. - Michael Somos Mar 02 2004
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REFERENCES
| W. Sierpinski, Pythagorean triangles, Dover Publications, Inc., Mineola, NY, 2003, p. 101 MR2002669
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LINKS
| G. M. Constantine, Multicolored parallelisms of isomorphic spanning trees, Discrete Mathematics and Theoretical Computer Science, 5(2002), 121-126.
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FORMULA
| a(1)=1, a(2)=2, a(3)=4, for n>=0, a(2n+3) = 4*2^n, a(2n+4) = 5*2^n.
Recurrence: for n>4, a(n) = 2a(n-2).
G.f.: [x(1+x)(1+x+x^2)]/[1-2x^2].
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CROSSREFS
| Cf. A029744, A029745. Union of A000079 and A020714.
Complement of A005767.
Sequence in context: A133075 A018433 A115831 * A018565 A018391 A018310
Adjacent sequences: A094955 A094956 A094957 * A094959 A094960 A094961
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Jun 01 2004
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EXTENSIONS
| Edited by T. D. Noe (noe(AT)sspectra.com) and M. F. Hasler (univ-ag.fr/~mhasler), Nov 12 2010
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