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Search: id:A114976
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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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2
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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
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OFFSET
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1,2
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COMMENT
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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
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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
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Sequence in context: A051612 A083456 A068058 this_sequence A085483 A038041 A097891
Adjacent sequences: A114973 A114974 A114975 this_sequence A114977 A114978 A114979
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 22 2006
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