A274535 a(n) = 5*sigma(n).

5, 15, 20, 35, 30, 60, 40, 75, 65, 90, 60, 140, 70, 120, 120, 155, 90, 195, 100, 210, 160, 180, 120, 300, 155, 210, 200, 280, 150, 360, 160, 315, 240, 270, 240, 455, 190, 300, 280, 450, 210, 480, 220, 420, 390, 360, 240, 620, 285, 465, 360, 490, 270, 600, 360, 600, 400, 450, 300, 840, 310, 480, 520, 635

Offset: 1

Author

Omar E. Pol, Jun 29 2016

Keywords

• nonn
• easy

Comments

5 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 72-degree-three-dimensional sector arises after the 72-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a five-pointed star formed by five 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 72-degree-zig-zag folding (rows: 1..28)
• Index entries for sequences related to sigma(n)

Crossrefs

k times sigma(n), k=1..6: A000203, A074400, A272027, A239050, this sequence, A274536.

Cf. A237593.

Programs

Maple

with(numtheory): seq(5*sigma(n), n=1..64);

Mathematica

Table[5 DivisorSigma[1, n], {n, 64}] (* Michael De Vlieger, Jul 04 2016 *)

PARI

a(n) = 5 * sigma(n);

Formula

a(n) = 5*A000203(n) = A000203(n) + A239050(n) = A074400(n) + A272027(n).

Dirichlet g.f.: 5*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 04 2016