A365414 - OEIS

A365414

a(n) = sigma(6*n+4). Sum of the divisors of 6*n+4, n >= 0.

7, 18, 31, 36, 56, 54, 90, 72, 98, 90, 127, 144, 140, 126, 180, 144, 217, 162, 248, 180, 224, 252, 270, 216, 266, 288, 378, 252, 308, 270, 360, 360, 399, 306, 434, 324, 504, 342, 450, 432, 434, 468, 511, 396, 476, 414, 720, 504, 518, 450, 620, 576, 560, 576, 630, 504, 756, 522, 756, 540

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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 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.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

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

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

MATHEMATICA

Table[DivisorSigma[1, 6*n + 4], {n, 0, 60}] (* Amiram Eldar, Sep 09 2023 *)

PROG

(PARI) a(n) = sigma(6*n+4); \\ Michel Marcus, Sep 08 2023

CROSSREFS

Partial sums give A365444.

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