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A065795
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Number of subsets of {1,2,...,n} that contain the average of their elements.
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0
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1, 2, 4, 6, 10, 16, 26, 42, 72, 124, 218, 390, 706, 1292, 2388, 4436, 8292, 15578, 29376, 55592, 105532, 200858, 383220, 732756, 1403848, 2694404, 5179938, 9973430, 19229826, 37125562, 71762396, 138871260, 269021848, 521666984
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = 1/2*sum_{i=1..n} (f(i) - 1) where f(i) = 1/n * sum_{d divides n and d is odd} 2^(n/d) * phi(d).
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EXAMPLE
| a(4)=6, since {1}, {2}, {3}, {4}, {1,2,3} and {2,3,4} contain their averages.
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MATHEMATICA
| Table[ Sum[a = Select[Divisors[i], OddQ[ # ] &]; Apply[ Plus, 2^(i/a)*EulerPhi[a]]/i, {i, 1, n}]/2, {n, 1, 34}]
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CROSSREFS
| Equals (n+A051293)/2.
Sequence in context: A094985 A128588 A023613 * A000801 A080105 A023557
Adjacent sequences: A065792 A065793 A065794 * A065796 A065797 A065798
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Dec 05 2001
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 15 2002
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