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A079526 a(n) = floor( exp(H_n)*log(H_n) ) - sigma(n).

%I A079526 #15 Sep 08 2022 08:45:08
%S A079526 -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,
%T A079526 26,13,42,3,46,18,36,32,41,1,57,38,45,14,65,14,69,32,41,51,78,5,75,42,
%U A079526 66,43,90,27,78,33,76,70,103,-2,107,76,71,51,98,41,120,65,98,53
%N A079526 a(n) = floor( exp(H_n)*log(H_n) ) - sigma(n).
%C A079526 M. Kaneko has shown that the Riemann hypothesis is equivalent to the assertion that a(n) > 0 for n > 60.
%H A079526 G. C. Greubel, <a href="/A079526/b079526.txt">Table of n, a(n) for n = 1..10000</a>
%H A079526 J. C. Lagarias, <a href="https://arxiv.org/abs/math/0008177">An elementary problem equivalent to the Riemann hypothesis</a>, arXiv:math/0008177 [math.NT], 2000-2001; Am. Math. Monthly 109 (#6, 2002), 534-543.
%t A079526 f[n_] := Floor[Exp[HarmonicNumber[n]]Log[HarmonicNumber[n]]] - DivisorSigma[1, n]; Array[f, 70] (* _Robert G. Wilson v_, Dec 17 2016 *)
%o A079526 (PARI) {h(n) = sum(k=1, n, 1/k)};
%o A079526 vector(80, n, floor( exp(h(n))*log(h(n))) - sigma(n,1) ) \\ _G. C. Greubel_, Jan 15 2019
%o A079526 (Magma) [Floor(Exp(HarmonicNumber(n))*Log(HarmonicNumber(n))) - DivisorSigma(1,n): n in [1..80]]; // _G. C. Greubel_, Jan 15 2019
%o A079526 (Sage) [floor(exp(harmonic_number(n))*log(harmonic_number(n))) - sigma(n,1) for n in (1..80)] # _G. C. Greubel_, Jan 15 2019
%Y A079526 H_n = sum of harmonic series (see A002387), sigma(n) = A000203.
%Y A079526 Cf. A057641, A058209, A079527.
%K A079526 sign
%O A079526 1,2
%A A079526 _N. J. A. Sloane_, Jan 22 2003