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A363161
Partial sums of A363031.
5
1, 9, 23, 43, 74, 106, 144, 188, 245, 317, 379, 447, 521, 601, 709, 821, 919, 1023, 1133, 1277, 1410, 1538, 1698, 1838, 2018, 2170, 2328, 2492, 2675, 2923, 3105, 3321, 3515, 3715, 3967, 4179, 4435, 4659, 4889, 5177, 5419, 5699, 5987, 6291, 6615, 6887, 7165, 7449, 7756, 8116, 8468, 8776, 9090, 9450, 9884
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)
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
Other sequences of the same family are A365442, A365444, A365446.
Sequence in context: A302906 A144390 A024843 * A183453 A296311 A159221
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, May 18 2023
STATUS
approved