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 A219729 #38 Mar 24 2025 06:13:40
%S A219729 1,2,3,5,6,8,9,11,14,16,17,20,21,23,26,30,31,34,35,39,42,44,45,49,54,
%T A219729 56,59,63,64,69,70,74,77,79,84,90,91,93,96,101,102,108,109,113,118,
%U A219729 120,121,127,134,139,142,146,147,153,158,165,168,170,171,177,178
%N A219729 Sum_{x <= n} largest divisor of x that is <= sqrt(x).
%C A219729 G. Tenenbaum proved that limit(log(a(n)/n^(3/2)))/log(log(n)) is -b with b = 1-(1+loglog 2)/log 2 = 0.08607... (same constant as in A027424 comment) (théorème 1).
%H A219729 Ivan Neretin, <a href="/A219729/b219729.txt">Table of n, a(n) for n = 1..10000</a>
%H A219729 Steven Finch, <a href="/A219729/a219729.pdf">Multiples and divisors</a>, January 27, 2004. [Cached copy, with permission of the author]
%H A219729 Gérald Tenenbaum, <a href="https://doi.org/10.1112/jlms/s2-14.3.521">Sur deux fonctions de diviseurs</a>, J. London Math. Soc. (1976) s2-14 (3): 521-526; <a href="https://tenenb.perso.math.cnrs.fr/PPP/Deux-fns.pdf">alternative copy</a>.
%t A219729 t = Table[d = Divisors[n]; d[[Ceiling[Length[d]/2]]], {n, 100}]; Accumulate[t] (* _T. D. Noe_, Nov 26 2012 *)
%Y A219729 Cf. A027424, A033676, A219730.
%K A219729 nonn
%O A219729 1,2
%A A219729 _Michel Marcus_, Nov 26 2012