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Search: id:A121594
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| A121594 |
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Numbers n such that n does not divide the denominator of the n-th alternating Harmonic number. |
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+0
6
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| 15, 28, 75, 77, 104, 187, 196, 203, 210, 222, 228, 235, 238, 328, 345, 375, 551, 620, 847, 888, 1036, 1107, 1204, 1349, 1352, 1372, 1391, 1430, 1457, 1469, 1470, 1498, 1666, 1687, 1855, 1875, 2133, 2301, 2425, 2440, 2556, 2678, 2948, 3179, 3337, 3477
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OFFSET
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1,1
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COMMENT
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Indices n such that A119788[n] is not equal to 1.
Also indices n such that numerators of n*H'[n]= A119787[n] and H'[n] = A058313[n] are different ( H'[n] is alternating harmonic number H'[n] = Sum[(-1)^(k+1)*1/k,{k,1,n}] ). The ratio of numerators A119787[n]/A058313[n] for n=1..400 is given in A119788[n]. A121595[n] = A119788[a(n)] is compressed version of A119788[n] (all 1 entries are excluded).
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MATHEMATICA
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Do[H=Sum[(-1)^(i+1)*1/i, {i, 1, n}]; a=Numerator[n*H]; b=Numerator[H]; If[ !Equal[a, b], Print[{n, a/b}]], {n, 1, 6000}]
f=0; Do[f=f+(-1)^(n+1)/n; If[ !IntegerQ[Denominator[f]/n], Print[n]], {n, 1, 100}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 02 2007
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CROSSREFS
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Cf. A119788, A119787, A058313, A121595.
Cf. A058312 = Denominator of the n-th alternating harmonic number, sum ((-1)^(k+1)/k, k=1..n). A074791 = numbers n such that n does not divide the denominator of the n-th Harmonic number.
Sequence in context: A045192 A039285 A043888 this_sequence A163286 A022997 A051121
Adjacent sequences: A121591 A121592 A121593 this_sequence A121595 A121596 A121597
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 09 2006
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