

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
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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



