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A065916
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Denominator[DivisorSigma[1,8*n^2]/DivisorSigma[1,4*n^2]].
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2
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7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 2047, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 8191, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 2047, 7, 31, 7, 127, 7, 31, 7, 511, 7, 31, 7, 127, 7, 31, 7, 32767, 7, 31, 7, 127, 7, 31, 7, 511, 7
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OFFSET
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1,1
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COMMENTS
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The sequence is not periodic. The denominators are always of the form -1+2^s.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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From Johannes W. Meijer, Feb 12 2013: (Start)
a((2*n-1)*2^p) = 2*4^(p+1) - 1 for p >= 0 and n >= 1. Observe that a(2^p) = A083420(p+1).
a(2^(p+3)*n + 2^(p+2) - 1) = a(2^(p+2)*n + 2^(p+1) - 1) for p >= 0. (End)
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EXAMPLE
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sigma[72]/sigma[36] = 15/7.
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MAPLE
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nmax:=73: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := 2*4^(p+1) - 1 od: od: seq(a(n), n=1..nmax); # [Johannes W. Meijer, Feb 12 2013]
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PROG
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(PARI) { for (n=1, 1000, a=denominator(sigma(8*n^2)/sigma(4*n^2)); write("b065916.txt", n, " ", a) ) } [Harry J. Smith, Nov 04 2009]
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CROSSREFS
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Cf. A000203, A028982, A065915, A220466.
Sequence in context: A196315 A156347 A221402 * A122654 A184121 A167768
Adjacent sequences: A065913 A065914 A065915 * A065917 A065918 A065919
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 28 2001
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STATUS
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approved
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