cp's OEIS Frontend

A365444 Partial sums of A365414.

%I A365444 #34 Oct 22 2023 16:58:26
%S A365444 7,25,56,92,148,202,292,364,462,552,679,823,963,1089,1269,1413,1630,
%T A365444 1792,2040,2220,2444,2696,2966,3182,3448,3736,4114,4366,4674,4944,
%U A365444 5304,5664,6063,6369,6803,7127,7631,7973,8423,8855,9289,9757,10268,10664,11140,11554,12274,12778
%N A365444 Partial sums of A365414.
%C A365444 Partial sums of the sum of the divisors of the numbers of the form 6*k + 4, k >= 0.
%C A365444 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 fourth wedge after n turns. The interesting fact is that for n >> 1 the geometric pattern in the fourth wedge of the spiral is similar to the geometric pattern of the second wedge but it is different from the other wedges.
%H A365444 OEIS Plot 2, <a href="https://oeis.org/plot2a?name1=A365444&amp;name2=A365442&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=matp&amp;drawlines=true">Plot pairs of A365444 and A365442</a>.
%H A365444 Omar E. Pol, <a href="/A365444/a365444.jpg">Plot 6. Area of the spiral in the six wedges after n turns</a>
%F A365444 a(n) = (5*Pi^2/9) * n^2 + O(n*log(n)). - _Amiram Eldar_, Sep 08 2023
%t A365444 Accumulate[Table[DivisorSigma[1, 6*n + 4], {n, 0, 50}]] (* _Amiram Eldar_, Sep 08 2023 *)
%o A365444 (PARI) a(n) = sum(k=0, n, sigma(6*k+4)); \\ _Michel Marcus_, Sep 08 2023
%Y A365444 Other sequences of the same family are A363161, A365442, A365446.
%Y A365444 Cf. A000203, A016957, A239660, A365414.
%K A365444 nonn,easy,less
%O A365444 0,1
%A A365444 _Omar E. Pol_, Sep 07 2023