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 A350801 #7 Jan 17 2022 14:04:50
%S A350801 0,0,0,1,2,3,6,5,10,10,14,9,28,11,22,27,34,15,48,17,56,41,38,21,96,38,
%T A350801 46,55,84,27,126,29,98,69,62,79,178,35,70,83,180,39,186,41,140,159,86,
%U A350801 45,280,82,164,111,168,51,246,131,264,125,110,57,444,59,118,233,258,157
%N A350801 a(n) = n*(tau(n) + 1) - 2*sigma(n) for n>=1, with a(0)=0.
%C A350801 Sum of the positive differences of the parts in the partitions of n into two parts such that the smaller part divides the larger (see example).
%H A350801 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A350801 For n > 0, a(n) = Sum_{d|n, d<n} (n - 2d).
%F A350801 For n > 0, a(n) = n*(A000005(n) + 1) - 2*A000203(n).
%e A350801 a(10) = 14; The partitions of 10 into two parts such that the smaller divides the larger are (1,9), (2,8), and (5,5). The sum of the positive differences of the parts is then (9-1) + (8-2) + (5-5) = 14.
%t A350801 Join[{0}, Table[n (1 + DivisorSigma[0, n]) - 2*DivisorSigma[1, n], {n, 100}]]
%Y A350801 Cf. A000005 (tau), A000203 (sigma), A023645, A032741.
%K A350801 nonn,easy
%O A350801 0,5
%A A350801 _Wesley Ivan Hurt_, Jan 16 2022