OFFSET
0,2
COMMENTS
Partial sums of the sum of the divisors of the numbers of the form 6*k + 1, k >= 0.
From Omar E. Pol, Sep 26 2023: (Start)
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 first wedge after n turns. The interesting fact is that for n >> 1 the geometric pattern in the first wedge is similar to the geometric pattern of the fifth wedge but it is different from the other wedges. (End)
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ Pi^2 * n^2 / 3. - Vaclav Kotesovec, Aug 31 2023
MATHEMATICA
Accumulate@ Array[DivisorSigma[1, 6 # + 1] &, 55, 0] (* Michael De Vlieger, Aug 27 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, sigma(6*k+1)); \\ Michel Marcus, Aug 28 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, May 18 2023
STATUS
approved