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A114976
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Number of subsets of {1,2,....,n} with an arithmetic mean that is an integer and also a divisor of n.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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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.
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CROSSREFS
| Sequence in context: A068058 A192233 A144943 * A085483 A038041 A197591
Adjacent sequences: A114973 A114974 A114975 * A114977 A114978 A114979
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 22 2006
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EXTENSIONS
| a(27)-a(38) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 10 2010
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