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A121594
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Numbers k such that k does not divide the denominator of the k-th alternating Harmonic number.
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7
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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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COMMENTS
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Indices k such that A119788(k) is not equal to 1.
Also indices k such that numerators of k*H'(k) = A119787(k) and H'(k) = A058313(k) are different (H'(k) is the alternating harmonic number H'(k) = Sum_{j=1..k} (-1)^(j+1)*1/j). The ratio of numerators A119787(k)/A058313(k) for k = 1..400 is given in A119788(k). A121595(k) = A119788(a(k)) is the compressed version of A119788(k) (all 1 entries are excluded).
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LINKS
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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, Jan 02 2007 *)
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CROSSREFS
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Cf. A058312 = Denominator of the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k. A074791 = numbers k such that k does not divide the denominator of the k-th Harmonic number.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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