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Search: id:A164978
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| A164978 |
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Number of divisors of n*(n+1)/2 that are >=n. |
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+0
4
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| 1, 1, 2, 2, 2, 2, 3, 4, 3, 2, 4, 4, 2, 4, 7, 4, 3, 3, 4, 7, 4, 2, 6, 8, 3, 4, 7, 4, 4, 4, 5, 9, 4, 4, 11, 6, 2, 4, 11, 6, 4, 4, 4, 11, 6, 2, 8, 11, 4, 6, 7, 4, 4, 7, 11, 11, 4, 2, 8, 8, 2, 6, 16, 11, 7, 4, 4, 7, 8, 4, 9, 9, 2, 6, 11, 8, 8, 4, 8, 18, 5, 2, 8, 15, 4, 4, 11, 6, 6, 11, 8, 7, 4, 4, 18, 10, 3, 8
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OFFSET
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1,3
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COMMENT
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a(n) = 2 <=> the set S = {1..n} has only one decomposition into smaller subsets with equal element sum.
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FORMULA
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a(n) = |{d|n*(n+1)/2 : d>=n}|.
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EXAMPLE
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a(6) = 2, because 6*7/2=21 with divisors {1,3,7,21}, but only 7 and 21 are >=6. S={1..6} has only one decomposition into smaller subsets with equal element sum: {1,6}, {2,5}, {3,4}.
a(7) = 3; 7*8/2=28 with divisors {1,2,4,7,14,28}, 3 of which are >=7. S={1..7} has 5 decompositions into smaller subsets with equal element sum.
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MAPLE
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with (numtheory): a:= n-> nops (select (x-> x>=n, divisors (n*(n+1) /2))): seq (a(n), n=1..120);
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CROSSREFS
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Cf. A164977, A035470.
Sequence in context: A082602 A127444 A069904 this_sequence A119789 A025424 A114775
Adjacent sequences: A164975 A164976 A164977 this_sequence A164979 A164980 A164981
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KEYWORD
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easy,nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 03 2009
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