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A079526
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a(n) = floor( exp(H_n)*log(H_n) ) - sigma(n).
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5
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-1, -2, -1, -2, 2, -2, 4, 0, 4, 2, 10, -3, 13, 6, 9, 4, 20, 2, 23, 4, 17, 16, 31, -3, 29, 21, 26, 13, 42, 3, 46, 18, 36, 32, 41, 1, 57, 38, 45, 14, 65, 14, 69, 32, 41, 51, 78, 5, 75, 42, 66, 43, 90, 27, 78, 33, 76, 70, 103, -2, 107, 76, 71, 51, 98, 41, 120, 65, 98, 53
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OFFSET
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1,2
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COMMENTS
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M. Kaneko has shown that the Riemann hypothesis is equivalent to the assertion that a(n) > 0 for n > 60.
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LINKS
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MATHEMATICA
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f[n_] := Floor[Exp[HarmonicNumber[n]]Log[HarmonicNumber[n]]] - DivisorSigma[1, n]; Array[f, 70] (* Robert G. Wilson v, Dec 17 2016 *)
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PROG
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(PARI) {h(n) = sum(k=1, n, 1/k)};
vector(80, n, floor( exp(h(n))*log(h(n))) - sigma(n, 1) ) \\ G. C. Greubel, Jan 15 2019
(Magma) [Floor(Exp(HarmonicNumber(n))*Log(HarmonicNumber(n))) - DivisorSigma(1, n): n in [1..80]]; // G. C. Greubel, Jan 15 2019
(Sage) [floor(exp(harmonic_number(n))*log(harmonic_number(n))) - sigma(n, 1) for n in (1..80)] # G. C. Greubel, Jan 15 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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