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A365412
a(n) = sigma(6*n+2). Sum of the divisors of 6*n+2, n >= 0.
1
3, 15, 24, 42, 42, 63, 60, 84, 93, 120, 96, 126, 114, 186, 132, 168, 171, 210, 216, 210, 186, 255, 204, 336, 222, 300, 240, 294, 324, 372, 336, 336, 294, 465, 312, 378, 330, 504, 432, 420, 399, 480, 384, 588, 480, 558, 420, 504, 540, 570, 456, 672, 474, 762, 492, 588, 549, 660, 744
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 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.
FORMULA
a(n) = A000203(6*n+2).
a(n) = A000203(A016933(n)).
MATHEMATICA
Table[DivisorSigma[1, 6*n + 2], {n, 0, 60}] (* Amiram Eldar, Sep 09 2023 *)
CROSSREFS
Other members of the same family are A363031 and A224613. Also 6*A098098.
Partial sums give A365442.
Sequence in context: A101133 A061386 A366209 * A057780 A274697 A129024
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 07 2023
STATUS
approved