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A365444
Partial sums of A365414.
4
7, 25, 56, 92, 148, 202, 292, 364, 462, 552, 679, 823, 963, 1089, 1269, 1413, 1630, 1792, 2040, 2220, 2444, 2696, 2966, 3182, 3448, 3736, 4114, 4366, 4674, 4944, 5304, 5664, 6063, 6369, 6803, 7127, 7631, 7973, 8423, 8855, 9289, 9757, 10268, 10664, 11140, 11554, 12274, 12778
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.
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
Other sequences of the same family are A363161, A365442, A365446.
Sequence in context: A155230 A155231 A155261 * A268239 A350222 A110672
KEYWORD
nonn,easy,less
AUTHOR
Omar E. Pol, Sep 07 2023
STATUS
approved