A325299 a(n) = 9 * sigma(n).

9, 27, 36, 63, 54, 108, 72, 135, 117, 162, 108, 252, 126, 216, 216, 279, 162, 351, 180, 378, 288, 324, 216, 540, 279, 378, 360, 504, 270, 648, 288, 567, 432, 486, 432, 819, 342, 540, 504, 810, 378, 864, 396, 756, 702, 648, 432, 1116, 513, 837, 648, 882, 486, 1080, 648, 1080, 720, 810, 540, 1512

Offset: 1

Author

Omar E. Pol, Jun 26 2019

Keywords

• nonn
• easy

Comments

9 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 40-degree-three-dimensional sector arises after the 40-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a nine-pointed star formed by nine rhombuses (see Links section).

Links

• Omar E. Pol, Diagram of the triangle A237593 before the 40-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, A274536, A319527, A319528.

Cf. A008591, A237593.

Programs

GAP

List([1..70],n->9*Sigma(n)); # After Muniru A Asiru

Maple

with(numtheory): seq(9*sigma(n), n=1..64);

Mathematica

9*DivisorSigma[1,Range[70]] (* After Harvey P. Dale *)

PARI

a(n) = 9 * sigma(n);

Formula

a(n) = 9*A000203(n) = 3*A272027(n).

a(n) = A000203(n) + A319528(n) = A074400(n) + A319527(n).

Dirichlet g.f.: 9*zeta(s-1)*zeta(s). - (After Ilya Gutkovskiy)