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a(n) = floor( exp(H_n)*log(H_n) ).
3

%I #14 Sep 08 2022 08:45:08

%S 0,1,3,5,8,10,12,15,17,20,22,25,27,30,33,35,38,41,43,46,49,52,55,57,

%T 60,63,66,69,72,75,78,81,84,86,89,92,95,98,101,104,107,110,113,116,

%U 119,123,126,129,132,135,138,141,144,147,150,153,156,160,163,166,169,172,175,178

%N a(n) = floor( exp(H_n)*log(H_n) ).

%H G. C. Greubel, <a href="/A079527/b079527.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 a[n_] := Exp[HarmonicNumber[n]] Log[HarmonicNumber[n]] // Floor;

%t Array[a, 64] (* _Jean-François Alcover_, Oct 08 2018 *)

%o (PARI) {h(n) = sum(k=1, n, 1/k)};

%o vector(80, n, floor( exp(h(n))*log(h(n))) ) \\ _G. C. Greubel_, Jan 15 2019

%o (Magma) [Floor(Exp(HarmonicNumber(n))*Log(HarmonicNumber(n))): n in [1..80]]; // _G. C. Greubel_, Jan 15 2019

%o (Sage) [floor(exp(harmonic_number(n))*log(harmonic_number(n))) for n in (1..80)] # _G. C. Greubel_, Jan 15 2019

%Y H_n = sum of harmonic series (see A002387).

%Y Cf. A079526.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jan 22 2003