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 A307042 #11 Jul 23 2019 07:49:44
%S A307042 1,3,6,12,17,23,30,40,52,62,73,91,104,118,133,155,172,196,215,245,266,
%T A307042 288,311,341,371,397,427,469,498,528,559,593,626,660,695,767,804,842,
%U A307042 881,931,972,1014,1057,1123,1183,1229,1276,1342,1398,1458,1509,1587,1640
%N A307042 Partial sums of the exponential divisors sum function: Sum_{k=1..n} esigma(k), where esigma is A051377.
%H A307042 Amiram Eldar, <a href="/A307042/b307042.txt">Table of n, a(n) for n = 1..10000</a>
%H A307042 J. Fabrykowski and M. V. Subbarao, <a href="https://doi.org/10.1515/9783110852790.201">The maximal order and the average order of multiplicative function sigma^(e)(n)</a>, in Théorie des nombres/Number theory (Quebec, PQ, 1987), 201-206, de Gruyter, Berlin, 1989.
%F A307042 a(n) ~ B * n^2, where B = 0.5682854937... (A275480).
%t A307042 esigma[n_] := Times @@ (Sum[ First[#]^d, {d, Divisors[Last[#]]}] & ) /@ FactorInteger[n]; Accumulate[Array[esigma, 60]] (* after _Jean-François Alcover_ at A051377 *)
%Y A307042 Cf. A024916, A051377, A064609, A275480.
%K A307042 nonn
%O A307042 1,2
%A A307042 _Amiram Eldar_, Mar 21 2019