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A065795 Number of subsets of {1,2,...,n} that contain the average of their elements. 0
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; text; internal format)
OFFSET

1,2

COMMENTS

Also the number of subsets of {1,2,...,n} with sum of entries divisible by the largest element (compare A000016). See the Palmer Melbane link for a bijection. - Joel B. Lewis, Nov 13 2014

LINKS

Table of n, a(n) for n=1..34.

Palmer Melbane, Art of Problem Solving thread. - Joel B. Lewis, Nov 13 2014

FORMULA

a(n) = 1/2*sum_{i=1..n} (f(i) - 1) where f(i) = 1/i * sum_{d divides i and d is odd} 2^(i/d) * phi(d).

EXAMPLE

a(4)=6, since {1}, {2}, {3}, {4}, {1,2,3} and {2,3,4} contain their averages.

MATHEMATICA

Table[ Sum[a = Select[Divisors[i], OddQ[ # ] &]; Apply[ Plus, 2^(i/a) * EulerPhi[a]]/i, {i, n}]/2, {n, 34}]

CROSSREFS

Equals (n+A051293)/2.

Sequence in context: A094985 A128588 A023613 * A000801 A080105 A023557

Adjacent sequences:  A065792 A065793 A065794 * A065796 A065797 A065798

KEYWORD

nonn

AUTHOR

John W. Layman, Dec 05 2001

EXTENSIONS

Edited and extended by Robert G. Wilson v, Nov 15 2002

STATUS

approved

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Last modified September 23 17:50 EDT 2017. Contains 292363 sequences.