|
%I #15 Dec 31 2020 11:11:15
%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 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).
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle A237593 before the 40-degree-zig-zag 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(s-1)*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
|
