cp's OEIS Frontend

A365442 Partial sums of A365412.

%I A365442 #50 May 05 2025 23:22:40
%S A365442 3,18,42,84,126,189,249,333,426,546,642,768,882,1068,1200,1368,1539,
%T A365442 1749,1965,2175,2361,2616,2820,3156,3378,3678,3918,4212,4536,4908,
%U A365442 5244,5580,5874,6339,6651,7029,7359,7863,8295,8715,9114,9594,9978,10566,11046,11604,12024,12528
%N A365442 Partial sums of A365412.
%C A365442 Partial sums of the sum of the divisors of the numbers of the form 6*k + 2, k >= 0.
%C A365442 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 + 1 turns. The interesting fact is that for n >> 1 the geometric pattern in the second wedge of the spiral is very similar to the geometric pattern of the fourth wedge but it is different from the other wedges. Note that the six wedge spiral shows more and better geometric patterns than the four quadrants spiral.
%C A365442 The graph is very close to the graph of A365444 (see the Links section).
%H A365442 Michael De Vlieger, <a href="/A365442/b365442.txt">Table of n, a(n) for n = 0..10000</a>
%H A365442 OEIS Plot 2, <a href="https://oeis.org/plot2a?name1=A365442&amp;name2=A365444&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=matp&amp;drawlines=true">Plot pairs of A365442 and A365444</a>
%H A365442 Omar E. Pol, <a href="/A363161/a363161.jpg">Plot 6. Area of the spiral in the six wedges</a>
%F A365442 a(n) = (5*Pi^2/9) * n^2 + O(n*log(n)). - _Amiram Eldar_, Sep 08 2023
%t A365442 Accumulate[Table[DivisorSigma[1, 6*n + 2], {n, 0, 50}]] (* _Amiram Eldar_, Sep 08 2023 *)
%o A365442 (PARI) a(n) = sum(k=0, n, sigma(6*k+2)); \\ _Michel Marcus_, Sep 09 2023
%Y A365442 Sequences of the same family are A363161, this sequence, A383403, A365444, A383405, A365446.
%Y A365442 Cf. A000203, A016933, A237593, A239660, A365412.
%K A365442 nonn,easy
%O A365442 0,1
%A A365442 _Omar E. Pol_, Sep 07 2023