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 A354801 #54 Oct 23 2023 02:00:34
%S A354801 1,3,7,11,19,24,36,44,57,68,88,95,119,136,156,172,204,218,254,271,301,
%T A354801 330,374,385,428,463,503,530,586,603,663,695,745,792,848,864,936,989,
%U A354801 1049,1078,1158,1187,1271,1318,1374,1439,1531,1550,1639,1695,1775,1832,1936,1977,2069,2116
%N A354801 n^2 minus the sum of all aliquot divisors of all positive integers <= n.
%C A354801 After the Dyck paths described in A237593 we can see that a(n) has a symmetric representation as follows: a(n) is the sum of the areas of two polygons. In the fourth quadrant of the infinite square grid the first polygon has a vertex at (0,0) and its area is equal to A000217(n). The second polygon appears if n >= 3 and it has a vertex at (n,-n) and its area is equal to A004125(n). So the area of the arrowhead-shaped polygon is equal to A153485(n). See the illustration of initial terms in the Links section.
%H A354801 Omar E. Pol, <a href="/A354801/a354801_1.jpg">Illustration of initial terms</a>
%F A354801 a(n) = A000217(n) + A004125(n).
%F A354801 a(n) = A000290(n) - A153485(n).
%F A354801 a(n) = A024916(n) + A004125(n) - A153485(n).
%t A354801 Accumulate[Table[3*n - 1 - DivisorSigma[1, n], {n, 1, 60}]] (* _Amiram Eldar_, Jun 12 2022 *)
%o A354801 (PARI) a(n) = n^2 - sum(k=1, n, sigma(k)-k); \\ _Michel Marcus_, Jun 13 2022
%o A354801 (Python)
%o A354801 from math import isqrt
%o A354801 def A354801(n): return n*(3*n+1)+(s:=isqrt(n))**2*(s+1)-sum((q:=n//k)*((k<<1)+q+1) for k in range(1,s+1))>>1 # _Chai Wah Wu_, Oct 22 2023
%Y A354801 Partial sums of A353190.
%Y A354801 Cf. A000217, A000290, A001065, A004125, A024916, A153485, A236104, A237591, A237593.
%K A354801 nonn,easy
%O A354801 1,2
%A A354801 _Omar E. Pol_, Jun 06 2022