This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A096580 #28 Apr 10 2019 02:55:40
%S A096580 2,3,28,8718,51426757439
%N A096580 a(n) = smallest m >= 2 such that Sum_{k=2..m} 1/(k*log(k)) >= n.
%C A096580 The sum diverges (see link), so a(n) is well-defined.
%H A096580 M. Goar, <a href="http://www.jstor.org/stable/2690790">Olivier and Abel on series convergence: An episode from early 19th century analysis</a>, Math. Mag., 72 (No. 5, 1999), 347-355.
%F A096580 Since Integral 1/(x*log(x)) dx = log log x, a(n) is close to e^(e^n) (cf. A096232, A096404, A016066).
%F A096580 a(n) is roughly exp(exp(n-k)), where k = 0.7946786454... - _Charles R Greathouse IV_, Jul 23 2007
%e A096580 For m = 27 the sum is 1.992912323604..., for m = 28 it is 2.0036302389..., so a(2) = 28.
%e A096580 For m = 8717 the sum is 2.999991290360..., for m = 8718 it is 3.0000039326..., so a(3) = 8718.
%t A096580 n = 0; m = 2; sum = 1/(m*Log[m]); lst = {};
%t A096580 While[n <= 3,
%t A096580 While[ sum < n, m++; sum += 1/(m*Log[m])];
%t A096580 AppendTo[lst, m]; n++]; lst (* _Robert Price_, Apr 09 2019 *)
%Y A096580 Cf. A016088.
%K A096580 nonn,more,hard
%O A096580 0,1
%A A096580 _N. J. A. Sloane_, Aug 13 2004
%E A096580 a(3) from _Robert G. Wilson v_, Aug 17 2004
%E A096580 a(4) from _Charles R Greathouse IV_, Jul 23 2007