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%I #17 Sep 25 2023 09:10:59
%S 3,15,24,42,42,63,60,84,93,120,96,126,114,186,132,168,171,210,216,210,
%T 186,255,204,336,222,300,240,294,324,372,336,336,294,465,312,378,330,
%U 504,432,420,399,480,384,588,480,558,420,504,540,570,456,672,474,762,492,588,549,660,744
%N a(n) = sigma(6*n+2). Sum of the divisors of 6*n+2, n >= 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 number of diamonds (or the area) added 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.
%F a(n) = A000203(6*n+2).
%F a(n) = A000203(A016933(n)).
%t Table[DivisorSigma[1, 6*n + 2], {n, 0, 60}] (* _Amiram Eldar_, Sep 09 2023 *)
%Y Other members of the same family are A363031 and A224613. Also 6*A098098.
%Y Partial sums give A365442.
%Y Cf. A000203, A016933, A239660.
%K nonn,easy
%O 0,1
%A _Omar E. Pol_, Sep 07 2023