%I
%S 9,27,36,63,54,108,72,135,117,162,108,252,126,216,216,279,162,351,180,
%T 378,288,324,216,540,279,378,360,504,270,648,288,567,432,486,432,819,
%U 342,540,504,810,378,864,396,756,702,648,432,1116,513,837,648,882,486,1080,648,1080,720,810,540,1512
%N a(n) = 9 * sigma(n).
%C 9 times the sum of the divisors of n.
%C a(n) is also the total number of horizontal rhombuses in the terraces of the nth level of an irregular stepped pyramid (starting from the top) in which the structure of every 40degreethreedimensional sector arises after the 40degreezigzag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a ninepointed star formed by nine rhombuses (see Links section).
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle A237593 before the 40degreezigzag folding (rows: 1..28)</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = 9*A000203(n) = 3*A272027(n).
%F a(n) = A000203(n) + A319528(n) = A074400(n) + A319527(n).
%F Dirichlet g.f.: 9*zeta(s1)*zeta(s).  (After _Ilya Gutkovskiy_)
%p with(numtheory): seq(9*sigma(n), n=1..64);
%t 9*DivisorSigma[1,Range[70]] (* After _Harvey P. Dale_ *)
%o (PARI) a(n) = 9 * sigma(n);
%o (GAP) List([1..70],n>9*Sigma(n)); # After _Muniru A Asiru_
%Y k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, A274536, A319527, A319528.
%Y Cf. A008591, A237593.
%K nonn,easy
%O 1,1
%A _Omar E. Pol_, Jun 26 2019
