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Search: id:A078709
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| A078709 |
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Integer part of the mean subinterval length in the partition of [0,n] by the divisors of n. |
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5
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| 1, 1, 1, 1, 2, 1, 3, 2, 3, 2, 5, 2, 6, 3, 3, 3, 8, 3, 9, 3, 5, 5, 11, 3, 8, 6, 6, 4, 14, 3, 15, 5, 8, 8, 8, 4, 18, 9, 9, 5, 20, 5, 21, 7, 7, 11, 23, 4, 16, 8, 12, 8, 26, 6, 13, 7, 14, 14, 29, 5, 30, 15, 10, 9, 16, 8, 33, 11, 17, 8, 35, 6, 36, 18, 12, 12, 19, 9, 39, 8, 16, 20, 41, 7, 21, 21, 21, 11
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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If the first occurrence of m in the sequence is greater than all preceding terms, the corresponding n is non-composite. - Donald Sampson (Marsquo(AT)hotmail.com), Dec 10 2003
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FORMULA
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a(n) = floor(n/tau(n)), where tau(n) is the number of divisors of n (A000005). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 26 2003
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EXAMPLE
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The divisors of 9 partition the closed interval [0,9] into subintervals [0,1), [1,3), [3,9], with lengths 1, 2, 6, respectively. The mean of these lengths has integer part = 3. Hence a(9) = 3.
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MATHEMATICA
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<< Statistics`DescriptiveStatistics` f[n_] := Module[{d, l, a, i}, d = Divisors[n]; l = Length[d]; a = {1}; For[i = 1, i <= l - 1, i++, a = Append[a, d[[i + 1]] - d[[i]]]]; a]; Table[Floor[Mean[f[i]]], {i, 1, 100}]
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CROSSREFS
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Cf. A078710.
Sequence in context: A007828 A070804 A104481 this_sequence A023022 A100677 A083290
Adjacent sequences: A078706 A078707 A078708 this_sequence A078710 A078711 A078712
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KEYWORD
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nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 19 2002
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