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a(n) = sigma(6*n+4). Sum of the divisors of 6*n+4, n >= 0.
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%I #16 Sep 25 2023 09:12:54

%S 7,18,31,36,56,54,90,72,98,90,127,144,140,126,180,144,217,162,248,180,

%T 224,252,270,216,266,288,378,252,308,270,360,360,399,306,434,324,504,

%U 342,450,432,434,468,511,396,476,414,720,504,518,450,620,576,560,576,630,504,756,522,756,540

%N a(n) = sigma(6*n+4). Sum of the divisors of 6*n+4, 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 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.

%F a(n) = A000203(6*n+4).

%F a(n) = A000203(A016957(n)).

%t Table[DivisorSigma[1, 6*n + 4], {n, 0, 60}] (* _Amiram Eldar_, Sep 09 2023 *)

%o (PARI) a(n) = sigma(6*n+4); \\ _Michel Marcus_, Sep 08 2023

%Y Partial sums give A365444.

%Y Other members of the same family are A363031 and A224613. Also 6*A098098.

%Y Cf. A000203, A016957, A363031.

%K nonn,easy,less

%O 0,1

%A _Omar E. Pol_, Sep 07 2023