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Search: id:A119788
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| A119788 |
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Ratio of the numerator of the product of n and the n-th alternating harmonic number n*H'[n] to the numerator of the n-th alternating harmonic number H'[n] = Sum[(-1)^(k+1)*1/k,{k,1,n}]. |
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+0
4
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13
(list; graph; listen)
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OFFSET
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1,15
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COMMENT
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Indices n such that a(n) is not equal to 1 are listed in A121594[n] = {15, 28, 75, 77, 104, 187, 196, 203, 210, 222, 228, 235, 238, 328, 345, 375, 551, 620, 847, 888, ...}. It appears that most a(n)>1 are the prime divisors of corresponding indices A121594[n]. The first and only composite a(n) up to a(6000) is a(1470) = 49 that also divides its index. Compressed version of a(n) (all 1 entries are excluded) is A121595[n] = a(A121594[n]) = {5, 7, 5, 11, 13, 17, 7, 29, 7, 37, 19, 47, 119, 41, 23, 5, 29, 31, 11, 37, 37, 41, 43, 71, 13, 7, 13, 13, 47, 13, 49, 7, 7, 7, ...}.
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LINKS
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Alexander Adamchuk, First 400 terms
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FORMULA
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a(n) = numerator[n*Sum[(-1)^(i+1)*1/i,{i, 1, n}]] / numerator[Sum[(-1)^(i+1)*1/i,{i, 1, n}]].
a(n) = A119787[n] / A058313[n].
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MATHEMATICA
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Numerator[Table[n*Sum[(-1)^(i+1)*1/i, {i, 1, n}], {n, 1, 600}]]/Numerator[Table[Sum[(-1)^(i+1)*1/i, {i, 1, n}], {n, 1, 600}]]
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CROSSREFS
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Cf. A058313.
Cf. A119787, A121594, A121595, A092579.
Sequence in context: A086464 A162298 A146306 this_sequence A059592 A098087 A165485
Adjacent sequences: A119785 A119786 A119787 this_sequence A119789 A119790 A119791
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 26 2006, Sep 21 2006
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