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Search: id:A138317
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| A138317 |
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Denominators of the squarefree totient analogs of the harmonic numbers F_n. |
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+0
6
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| 1, 1, 2, 2, 4, 4, 12, 12, 12, 3, 30, 30, 20, 60, 120, 120, 240, 240, 720, 720, 720, 720, 7920, 7920, 7920, 7920, 7920, 7920, 55440, 55440, 55440, 55440, 55440, 27720, 3465, 3465, 4620, 13860, 27720, 27720, 13860, 6930, 3465, 3465, 3465, 6930, 79695, 79695
(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)] where mu(k) is the Mobius function and phi(k) is Euler's Totient function.
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EXAMPLE
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Denominators of F_n, e.g. - F_1 = (1/1), F_2=(1/1+1/1),...F_11=(1/1+1/1+1/2+0+1/4+1/2+1/6+0+0+1/4+1/10)
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MATHEMATICA
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Table[Denominator[Sum[MoebiusMu[k]^2/EulerPhi[k], {k, 1, n}]], {n, 1, 60}]
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CROSSREFS
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Cf. A138312, A138313, A138312, A138316, A138320, A138321, A083343, A001620.
Sequence in context: A057784 A081164 A125553 this_sequence A103659 A069947 A051547
Adjacent sequences: A138314 A138315 A138316 this_sequence A138318 A138319 A138320
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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 13 2008, Mar 27 2008
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