A365412 a(n) = sigma(6*n+2). Sum of the divisors of 6*n+2, n >= 0.

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.

Links

Table of n, a(n) for n=0..58.

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.

Cf. A000203, A016933, A239660.

Sequence in context: A101133 A061386 A366209 * A057780 A274697 A129024

Adjacent sequences: A365409 A365410 A365411 * A365413 A365414 A365415

Keyword

nonn,easy

Author

Omar E. Pol, Sep 07 2023

Status

approved