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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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6
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Alan Sutcliffe, Divisors and Common Factors in Sets of Integers, awaiting publication.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..200
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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FORMULA
| a(n) = 1 + Sum_{k=1..A036234(n)} A186974(n,k) if n>0; a(0) = 1.
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EXAMPLE
| 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
| Cf. 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.
Cf. A036234, A186974.
Sequence in context: A027677 A103787 A032473 * A175841 A171647 A089821
Adjacent sequences: A084419 A084420 A084421 * A084423 A084424 A084425
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KEYWORD
| nonn
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AUTHOR
| Matthew Vandermast (ghodges14(AT)comcast.net), Jun 26 2003
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EXTENSIONS
| More terms from Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 12 2003
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