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 A349237 #9 Dec 02 2021 00:55:46
%S A349237 1,3,6,3,1,2,9,8,9,8,0
%N A349237 Decimal expansion of lim_{x->oo} (1/x) * Sum_{c(k+1) <= x} (c(k+1) - c(k))^2, where c(k) = A004709(k) is the k-th cubefree number.
%C A349237 Huxley (1997) proved the existence of this limit and Mossinghoff et al. (2021) calculated its first 11 decimal digits.
%C A349237 Let g(n) = A349236(n) be the sequence of gaps between cubefree numbers. The asymptotic mean of g is <g> = zeta(3) (A002117). The second raw moment of g is <g^2> = zeta(3) * 1.3631298980... = 1.638559703..., the second central moment, or variance, of g is <g^2> - <g>^2 = 0.193618905... and the standard deviation is sqrt(<g^2> - <g>^2) = 0.440021482...
%D A349237 M. N. Huxley, Moments of differences between square-free numbers, in G. R. H. Greaves, G. Harman and M. N. Huxley (eds.), Sieve methods, exponential sums, and their applications in number theory (Cardiff, 1995), London Math. Soc. Lecture Note Series, Vol. 237, Cambridge Univ. Press, Cambridge, 1997, pp. 187-204.
%H A349237 Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, <a href="https://doi.org/10.1090/mcom/3581">The distribution of k-free numbers</a>, Mathematics of Computation, Vol. 90, No. 328 (2021), pp. 907-929; <a href="https://arxiv.org/abs/1912.04972">arXiv preprint</a>, arXiv:1912.04972 [math.NT], 2019-2020.
%e A349237 1.3631298980...
%Y A349237 Cf. A002117, A004709, A349232, A349236.
%K A349237 nonn,cons,more
%O A349237 1,2
%A A349237 _Amiram Eldar_, Nov 11 2021