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A120263
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Ratio of the numerator of n*HarmonicNumber[n] to the numerator of HarmonicNumber[n]: A096617(n)/A001008(n).
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0
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1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| a(n) is not equal to 1 for n belongs to A074791 - numbers n such that n does not divide the denominator of the n-th harmonic number. a(n) is almost always equal to 1 except for n=6,18,20,21,33,42,54,.. when a(n) seems to be equal to a prime divisor of n. a(n) could be equal to a squared prime divisor of n as for n=100,294,500,847,..
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FORMULA
| a(n) = A096617(n)/A001008(n) = numerator[n*Sum[1/i,{i,1,n}]] / numerator[Sum[1/i,{i,1,n}]].
a(n)= n / gcd(denominator(H(n)),n), where H(n) = sum(1/k, k=1..n). [From Gary Detlefs, Sep 05 2011]
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MATHEMATICA
| Numerator[Table[n*Sum[1/i, {i, 1, n}], {n, 1, 500}]]/Numerator[Table[Sum[1/i, {i, 1, n}], {n, 1, 500}]]
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CROSSREFS
| Cf. A096617, A001008, A074791.
Sequence in context: A202150 A093818 A097031 * A030580 A030579 A030578
Adjacent sequences: A120260 A120261 A120262 * A120264 A120265 A120266
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KEYWORD
| frac,nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 26 2006
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