%I #31 Sep 26 2023 16:58:54
%S 3,18,42,84,126,189,249,333,426,546,642,768,882,1068,1200,1368,1539,
%T 1749,1965,2175,2361,2616,2820,3156,3378,3678,3918,4212,4536,4908,
%U 5244,5580,5874,6339,6651,7029,7359,7863,8295,8715,9114,9594,9978,10566,11046,11604,12024,12528
%N Partial sums of A365412.
%C Partial sums of the sum of the divisors of the numbers of the form 6*k + 2, k >= 0.
%C Consider a spiral similar to the spiral described in A239660 but instead of having four quadrants on the square grid the new spiral has six wedges on the triangular grid. A "diamond" formed by two adjacent triangles has area 1. a(n) is the total number of diamonds (or the total area) in the second wedge after n turns. The interesting fact is that for n >> 1 the geometric pattern in the second wedge of the spiral is similar to the geometric pattern of the fourth wedge but it is different from the other wedges.
%C The graph is very close to the graph of A365444 (see the Links section).
%H OEIS Plot 2, <a href="https://oeis.org/plot2a?name1=A365442&name2=A365444&tform1=untransformed&tform2=untransformed&shift=0&radiop1=matp&drawlines=true">Plot pairs of A365442 and A365444</a>
%F a(n) = (5*Pi^2/9) * n^2 + O(n*log(n)). - _Amiram Eldar_, Sep 08 2023
%t Accumulate[Table[DivisorSigma[1, 6*n + 2], {n, 0, 50}]] (* _Amiram Eldar_, Sep 08 2023 *)
%o (PARI) a(n) = sum(k=0, n, sigma(6*k+2)); \\ _Michel Marcus_, Sep 09 2023
%Y Cf. A000203, A016933, A363161, A365412, A365444, A365446.
%K nonn,easy
%O 0,1
%A _Omar E. Pol_, Sep 07 2023