

A114976


Number of subsets of {1,2,....,n} with an arithmetic mean that is an integer and also a divisor of n.


3



1, 2, 2, 5, 2, 14, 2, 30, 11, 80, 2, 280, 2, 764, 128, 2557, 2, 9036, 2, 29656, 1958, 103134, 2, 373454, 119, 1300824, 36992, 4681568, 2, 17119030, 2, 61799636, 758982, 226451040, 2180, 837469677, 2, 3084255132, 16391220, 11451833394, 2, 42746493556, 2
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OFFSET

1,2


COMMENTS

a(n) <= A051293(n);
a(n) = 2 iff n is prime, just as for the number of divisors of n and also, at least for the very first terms, a(n)=odd iff n is a square: these observations migth suggest conjectures on a deeper relationship with A000005.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..100


EXAMPLE

a(9) = 11: {1}, {3}, {9}, {1,5}, {2,4}, {1,2,6}, {1,3,5}, {2,3,4}, {1,2,3,6}, {1,2,4,5} and {1,2,3,4,5}, e.g. also {1,4,7} has an integral arithmetic mean, but (1+4+7)/3 = 4 is not a divisor of 9.


MAPLE

b:= proc(n, m, s, c) option remember; `if`(n=0,
`if`(c>0 and denom(s)=1 and irem(m, s)=0, 1, 0),
b(n1, m, s, c)+b(n1, m, (s*c+n)/(c+1), c+1))
end:
a:= proc(n) option remember; forget (b); b(n$2, 0$2) end:
seq(a(n), n=1..50); # Alois P. Heinz, Jul 15 2019


CROSSREFS

Cf. A000005, A051293.
Sequence in context: A068058 A192233 A144943 * A085483 A271654 A271622
Adjacent sequences: A114973 A114974 A114975 * A114977 A114978 A114979


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Feb 22 2006


EXTENSIONS

a(27)a(38) from Donovan Johnson, Jun 10 2010
a(39)a(43) from Alois P. Heinz, Jul 15 2019


STATUS

approved



