OFFSET
0,1
COMMENTS
Partial sums of the sum of the divisors of the numbers of the form 6*k + 4, k >= 0.
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 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
FORMULA
a(n) = (5*Pi^2/9) * n^2 + O(n*log(n)). - Amiram Eldar, Sep 08 2023
MATHEMATICA
Accumulate[Table[DivisorSigma[1, 6*n + 4], {n, 0, 50}]] (* Amiram Eldar, Sep 08 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, sigma(6*k+4)); \\ Michel Marcus, Sep 08 2023
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Omar E. Pol, Sep 07 2023
STATUS
approved