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3, 18, 42, 84, 126, 189, 249, 333, 426, 546, 642, 768, 882, 1068, 1200, 1368, 1539, 1749, 1965, 2175, 2361, 2616, 2820, 3156, 3378, 3678, 3918, 4212, 4536, 4908, 5244, 5580, 5874, 6339, 6651, 7029, 7359, 7863, 8295, 8715, 9114, 9594, 9978, 10566, 11046, 11604, 12024, 12528
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OFFSET
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0,1
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COMMENTS
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Partial sums of the sum of the divisors of the numbers of the form 6*k + 2, 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 second wedge after n turns. The interesting fact is that for n >> 1 the geometric pattern in the second wedge of the spiral is similar to the geometric pattern of the fourth wedge but it is different from the other wedges.
The graph is very close to the graph of A365444 (see the Links section).
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LINKS
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FORMULA
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a(n) = (5*Pi^2/9) * n^2 + O(n*log(n)). - Amiram Eldar, Sep 08 2023
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MATHEMATICA
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Accumulate[Table[DivisorSigma[1, 6*n + 2], {n, 0, 50}]] (* Amiram Eldar, Sep 08 2023 *)
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PROG
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(PARI) a(n) = sum(k=0, n, sigma(6*k+2)); \\ Michel Marcus, Sep 09 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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