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Search: id:A138321
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| A138321 |
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Denominators of the difference between the squarefree totient analogs of the harmonic numbers and the harmonic numbers: F_n-H_n. |
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+0
4
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| 1, 1, 12, 24, 240, 80, 560, 3360, 30240, 7560, 831600, 831600, 93600, 21621600, 6177600, 12355200, 2940537600, 980179200, 55870214400, 2234808576, 3724680960, 177365760, 49597067520, 29758240512, 3719780064000
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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F_n-H_n approaches a constant, 'kappa', conjectured to be equivalent to the difference of B_3-gamma, where B_3 is Mertens' 3^rd constant and gamma is Euler's constant
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LINKS
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Dick Boland, An Analog of the Harmonic Numbers Over the Squarefree Integers
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FORMULA
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a(n)=Denominator[(sum(k=1 to n)mu^2(k)/phi(k))-H_n] where mu(k) is the Mobius function, phi(k) is Euler's Totient function and H_n is the n^th Harmonic Number.
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EXAMPLE
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Denominators of F_n-H_n, e.g. - F_1-H_1 = (1/1-1/1), F_2=((1/1-1/1)+(1/1-1/2)),...
F_11=((1/1-1/1)+(1/1-1/2)+(1/2-1/3)+(0-1/4)+(1/4-1/5)+(1/2-1/6)+(1/6-1/7)+(0-1/8)+(0-1/9)+(1/4-1/10)+(1/10-1/11) )
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MATHEMATICA
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Table[Denominator[Sum[MoebiusMu[k]^2/EulerPhi[k], {k, 1, n}]-HarmonicNumber[n]], {n, 1, 60}]
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CROSSREFS
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Cf. A138312, A138313, A138312, A138316, A138317, A138320, A083343, A001620.
Adjacent sequences: A138318 A138319 A138320 this_sequence A138322 A138323 A138324
Sequence in context: A130163 A002167 A058994 this_sequence A033165 A042851 A041280
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KEYWORD
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frac,nonn
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AUTHOR
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Dick Boland (abstract(AT)imathination.org), Mar 14 2008, Mar 27 2008
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