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%I #39 Oct 08 2023 09:32:12
%S 1,9,23,43,74,106,144,188,245,317,379,447,521,601,709,821,919,1023,
%T 1133,1277,1410,1538,1698,1838,2018,2170,2328,2492,2675,2923,3105,
%U 3321,3515,3715,3967,4179,4435,4659,4889,5177,5419,5699,5987,6291,6615,6887,7165,7449,7756,8116,8468,8776,9090,9450,9884
%N Partial sums of A363031.
%C Partial sums of the sum of the divisors of the numbers of the form 6*k + 1, k >= 0.
%C From _Omar E. Pol_, Sep 26 2023: (Start)
%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 first wedge after n turns. The interesting fact is that for n >> 1 the geometric pattern in the first wedge is similar to the geometric pattern of the fifth wedge but it is different from the other wedges. (End)
%H Michael De Vlieger, <a href="/A363161/b363161.txt">Table of n, a(n) for n = 0..10000</a>
%H Omar E. Pol, <a href="/A363161/a363161.jpg">Plot 6. Area of the spiral in the six wedges after n turns</a>
%F a(n) ~ Pi^2 * n^2 / 3. - _Vaclav Kotesovec_, Aug 31 2023
%t Accumulate@ Array[DivisorSigma[1, 6 # + 1] &, 55, 0] (* _Michael De Vlieger_, Aug 27 2023 *)
%o (PARI) a(n) = sum(k=0, n, sigma(6*k+1)); \\ _Michel Marcus_, Aug 28 2023
%Y Other sequences of the same family are A365442, A365444, A365446.
%Y Cf. A016921, A239660, A363031.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, May 18 2023