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A365414
a(n) = sigma(6*n+4). Sum of the divisors of 6*n+4, n >= 0.
1
7, 18, 31, 36, 56, 54, 90, 72, 98, 90, 127, 144, 140, 126, 180, 144, 217, 162, 248, 180, 224, 252, 270, 216, 266, 288, 378, 252, 308, 270, 360, 360, 399, 306, 434, 324, 504, 342, 450, 432, 434, 468, 511, 396, 476, 414, 720, 504, 518, 450, 620, 576, 560, 576, 630, 504, 756, 522, 756, 540
OFFSET
0,1
COMMENTS
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 number of diamonds (or the area) added 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) = A000203(6*n+4).
a(n) = A000203(A016957(n)).
MATHEMATICA
Table[DivisorSigma[1, 6*n + 4], {n, 0, 60}] (* Amiram Eldar, Sep 09 2023 *)
PROG
(PARI) a(n) = sigma(6*n+4); \\ Michel Marcus, Sep 08 2023
CROSSREFS
Partial sums give A365444.
Other members of the same family are A363031 and A224613. Also 6*A098098.
Sequence in context: A061876 A341008 A103571 * A103572 A049532 A156619
KEYWORD
nonn,easy,less
AUTHOR
Omar E. Pol, Sep 07 2023
STATUS
approved