A274536 a(n) = 6 * sigma(n).

6, 18, 24, 42, 36, 72, 48, 90, 78, 108, 72, 168, 84, 144, 144, 186, 108, 234, 120, 252, 192, 216, 144, 360, 186, 252, 240, 336, 180, 432, 192, 378, 288, 324, 288, 546, 228, 360, 336, 540, 252, 576, 264, 504, 468, 432, 288, 744, 342, 558, 432, 588, 324, 720, 432, 720, 480, 540, 360, 1008, 372, 576, 624, 762

Offset: 1

Author

Omar E. Pol, Jun 29 2016

Keywords

• nonn
• easy

Comments

6 times the sum of the divisors of n.

a(n) is also the total number of horizontal rhombuses in the terraces of the n-th level of an irregular stepped pyramid (starting from the top) in which the structure of every 60-degree-three-dimensional sector arises after the 60-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a six-pointed star formed by six rhombuses (see Links section).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Omar E. Pol, Diagram of the triangle before the 60-degree-zig-zag folding (rows: 1..28)
• Index entries for sequences related to sigma(n)

Crossrefs

k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, this sequence, A319527, A319528.

Cf. A237593, A283118.

Programs

Maple

with(numtheory): seq(6*sigma(n), n=1..64);

Mathematica

6DivisorSigma[1, Range[50]] (* Alonso del Arte, Jul 04 2016 *)

PARI

a(n) = 6 * sigma(n);

Formula

a(n) = 6*A000203(n) = 3*A074400(n) = 2*A272027(n).

a(n) = A000203(n) + A274535(n) = A074400(n) + A239050(n).

Dirichlet g.f.: 6*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 04 2016

Conjecture: a(n) = sigma(5*n) = A283118(n) iff n is not a multiple of 5. - Omar E. Pol, Oct 02 2018