A274535 - OEIS

%I #40 Dec 31 2020 11:11:15

%S 5,15,20,35,30,60,40,75,65,90,60,140,70,120,120,155,90,195,100,210,

%T 160,180,120,300,155,210,200,280,150,360,160,315,240,270,240,455,190,

%U 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

%N a(n) = 5*sigma(n).

%C 5 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 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).

%H Antti Karttunen, <a href="/A274535/b274535.txt">Table of n, a(n) for n = 1..10000</a>

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle before the 72-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) = 5*A000203(n) = A000203(n) + A239050(n) = A074400(n) + A272027(n).

%F Dirichlet g.f.: 5*zeta(s-1)*zeta(s). - _Ilya Gutkovskiy_, Jul 04 2016

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

%t Table[5 DivisorSigma[1, n], {n, 64}] (* _Michael De Vlieger_, Jul 04 2016 *)

%o (PARI) a(n) = 5 * sigma(n);

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

%Y Cf. A237593.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Jun 29 2016