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A085945
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Number of subsets of {1,2,..,n} with relatively prime elements.
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4
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1, 2, 5, 11, 26, 53, 116, 236, 488, 983, 2006, 4016, 8111, 16238, 32603, 65243, 130778, 261566, 523709, 1047479, 2095988, 4192115, 8386418, 16772858, 33550058, 67100393, 134209001, 268418531, 536853986, 1073707991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equals row sums of triangle A143446 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 15 2008]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..300
Melvyn B. Nathanson, Affine Invariants, Relatively Prime Sets and a Phi Function for Subsets of {1, 2, ..., n}, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A1.
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FORMULA
| Partial sums of A000740. G.f.: 1/(1-x)* Sum_{k>0} mu(k)*x^k/(1-2*x^k).
a(n) = 2^n - A109511(n) - 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 01 2005
a(n)=Sum_{k=1,2,...,n}: mu(k)*(2^floor(n/k)-1). - Geoffrey Critzer, Jan 03 2012
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EXAMPLE
| For n=4 there are 11 such subsets: {1}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,2,4}, {1,3,4}, {2,3,4}, {1,2,3,4}.
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MATHEMATICA
| Table[Sum[MoebiusMu[k] (2^Floor[n/k] - 1), {k, 1, n}], {n, 1, 31}] (* Geoffrey Critzer, Jan 03 2012 *)
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CROSSREFS
| A143446 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 15 2008]
Sequence in context: A127075 A053429 A104237 * A005469 A159929 A026787
Adjacent sequences: A085942 A085943 A085944 * A085946 A085947 A085948
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KEYWORD
| nonn,changed
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2003
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