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Search: id:A084422
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| A084422 |
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Number of subsets of integers 1 through n (including null set) containing no pair of integers that share a common factor. |
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+0
4
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| 1, 2, 4, 8, 12, 24, 28, 56, 72, 104, 116, 232, 248, 496, 544, 616, 728, 1456, 1520, 3040, 3232, 3616, 3872, 7744, 8000, 11168, 11904, 14656, 15488, 30976, 31232, 62464, 69888, 76160, 80256, 89856, 91648, 183296, 192640, 208640, 214272, 428544
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting publication.
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LINKS
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N. J. Calkin and A. Granville, On the number of coprime-free sets, Number Theory: New York Seminar 1991-1995 (eds. D. Chudnovsky, et.al.), Springer-Verlag (1996).
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EXAMPLE
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Exactly 4 of the 2^4=16 subsets of the integers from 1 through 4 contain a pair of integers that share a common factor; these are {2,4}, {1,2,4}, {2,3,4} and {1,2,3,4}. The other 12 subsets do not; hence a(4)=12.
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CROSSREFS
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A051026 gives the number of primitive subsets. A087080 gives the number of elements in coprime subsets. A087081 gives the sum of the elements in coprime subsets.
Sequence in context: A027677 A103787 A032473 this_sequence A089821 A097942 A004653
Adjacent sequences: A084419 A084420 A084421 this_sequence A084423 A084424 A084425
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KEYWORD
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nonn
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AUTHOR
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Matthew Vandermast (ghodges14(AT)comcast.net), Jun 26 2003
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EXTENSIONS
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More terms from Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 12 2003
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