A326122 - OEIS

%I #18 Sep 08 2022 08:46:24

%S 10,30,40,70,60,120,80,150,130,180,120,280,140,240,240,310,180,390,

%T 200,420,320,360,240,600,310,420,400,560,300,720,320,630,480,540,480,

%U 910,380,600,560,900,420,960,440,840,780,720,480,1240,570,930,720,980,540,1200,720,1200,800,900,600,1680,620,960

%N a(n) = 10 * sigma(n).

%C 10 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) where the structure of every 36-degree-three-dimensional sector arises after the 36-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a 10-pointed star formed by 10 rhombuses (see Links section).

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle A237593 before the 36-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) = 10*A000203(n) = 5*A074400(n) = 2*A274535(n).

%F a(n) = A000203(n) + A325299(n) = A074400(n) + A319528(n).

%F Dirichlet g.f.: 10*zeta(s-1)*zeta(s). - (After _Ilya Gutkovskiy_)

%p with(numtheory): seq(10*sigma(n), n=1..64);

%t 10*DivisorSigma[1,Range[70]] (* After _Harvey P. Dale_ *)

%o (PARI) a(n) = 10 * sigma(n);

%o (GAP) List([1..70],n->10*Sigma(n)); # After _Muniru A Asiru_

%o (Magma) [10*DivisorSigma(1, n): n in [1..70]]; // _Vincenzo Librandi_, Jul 26 2019

%Y k times sigma(n), k=1..9: A000203, A074400, A272027, A239050, A274535, A274536, A319527, A319528, A325299.

%Y Cf. A008592, A033583, A124080, A124252, A142342, A153780, A237593.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Jul 13 2019