A365412 a(n) = sigma(6*n+2). Sum of the divisors of 6*n+2, n >= 0.

3, 15, 24, 42, 42, 63, 60, 84, 93, 120, 96, 126, 114, 186, 132, 168, 171, 210, 216, 210, 186, 255, 204, 336, 222, 300, 240, 294, 324, 372, 336, 336, 294, 465, 312, 378, 330, 504, 432, 420, 399, 480, 384, 588, 480, 558, 420, 504, 540, 570, 456, 672, 474, 762, 492, 588, 549, 660, 744

Offset: 0

Author

Omar E. Pol, Sep 07 2023

Keywords

• nonn
• easy

Comments

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.

Crossrefs

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

Partial sums give A365442.

Cf. A000203, A016933, A239660.

Programs

Mathematica

Table[DivisorSigma[1, 6*n + 2], {n, 0, 60}] (* Amiram Eldar, Sep 09 2023 *)

Formula

a(n) = A000203(6*n+2).

a(n) = A000203(A016933(n)).