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 A365446 #25 Apr 27 2025 14:48:17
%S A365446 12,40,79,139,211,302,398,522,642,810,954,1149,1317,1541,1775,2027,
%T A365446 2243,2523,2763,3123,3435,3771,4059,4462,4834,5226,5589,6069,6429,
%U A365446 6975,7359,7867,8335,8839,9415,10015,10471,11031,11577,12321,12825,13553,14081,14801,15521,16193,16769,17588,18272,19140,19842
%N A365446 Partial sums of A224613.
%C A365446 Partial sums of the sum of the divisors of the nonzero multiples of 6.
%C A365446 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 sixth wedge after n turns. Note that the six wedge spiral shows more and better geometric patterns than the four quadrants spiral. - _Omar E. Pol_, Apr 26 2025
%H A365446 Omar E. Pol, <a href="/A363161/a363161.jpg">Plot 6. Area of the spiral in the six wedges</a>
%F A365446 a(n) = (55*Pi^2/72) * n^2 + O(n*log(n)). - _Amiram Eldar_, Sep 07 2023
%t A365446 Accumulate[Table[DivisorSigma[1, 6*n], {n, 1, 50}]] (* _Amiram Eldar_, Sep 07 2023 *)
%o A365446 (Python)
%o A365446 from math import prod
%o A365446 from collections import Counter
%o A365446 from sympy import factorint
%o A365446 def A365446(n): return sum(prod((p**(e+1)-1)//(p-1) for p, e in (Counter(factorint(m))+Counter([2,3])).items()) for m in range(1,n+1)) # _Chai Wah Wu_, Sep 07 2023
%Y A365446 Sequences of the same family are A363161, A365442, A365444, A383405, this sequence.
%Y A365446 Cf. A000203, A008588, A224613, A237593, A239660.
%K A365446 nonn,easy
%O A365446 1,1
%A A365446 _Omar E. Pol_, Sep 04 2023