cp's OEIS Frontend

A057640 a(n) = floor(H(n) + exp(H(n))*log(H(n))), where H(n) = Sum_{k=1..n} 1/k.

%I A057640 #26 May 17 2022 17:52:00
%S A057640 1,3,5,7,10,12,15,17,20,23,25,28,31,33,36,39,41,44,47,50,53,56,58,61,
%T A057640 64,67,70,73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,
%U A057640 124,127,130,133,136,139,142,145,149,152,155,158,161
%N A057640 a(n) = floor(H(n) + exp(H(n))*log(H(n))), where H(n) = Sum_{k=1..n} 1/k.
%H A057640 David A. Corneth, <a href="/A057640/b057640.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A057640 Masazumi Honda and Takuya Yoda, <a href="https://arxiv.org/abs/2203.17091">String theory, N = 4 SYM and Riemann hypothesis</a>, arXiv:2203.17091 [hep-th], 2022.
%H A057640 Jeffrey C. Lagarias, <a href="http://arXiv.org/abs/math.NT/0008177">An elementary problem equivalent to the Riemann hypothesis</a>, Am. Math. Monthly 109 (#6, 2002), 534-543.
%H A057640 OEIS Plot 2, <a href="https://oeis.org/plot2a?name1=A057640&amp;name2=A000203&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=matp&amp;drawlines=true">A057640 vs A000203</a>
%t A057640 hn[n_]:=Module[{h=HarmonicNumber[n]},Floor[h+Exp[h]Log[h]]]; Array[hn,60] (* _Harvey P. Dale_, Aug 02 2013 *)
%o A057640 (PARI) first(n) = { my(h = 0, res = vector(n)); for(i = 1, n, print1(i", "); h+=1/i; res[i] = floor(h+exp(h)*log(h)) ); res } \\ _David A. Corneth_, Apr 28 2022
%Y A057640 Cf. A000203, A001008, A002805, A057641.
%K A057640 nonn,nice,easy
%O A057640 1,2
%A A057640 _N. J. A. Sloane_, Oct 12 2000