A319527 - OEIS

%I #16 Dec 31 2020 11:11:15

%S 7,21,28,49,42,84,56,105,91,126,84,196,98,168,168,217,126,273,140,294,

%T 224,252,168,420,217,294,280,392,210,504,224,441,336,378,336,637,266,

%U 420,392,630,294,672,308,588,546,504,336,868,399,651,504,686,378,840,504,840,560,630,420,1176,434,672,728,889

%N a(n) = 7 * sigma(n).

%C 7 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 (360/7)-degree-three-dimensional sector arises after the (360/7)-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a seven-pointed star formed by seven rhombuses (see Links section).

%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle A237593 before the (360/7)-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) = 7*A000203(n).

%F a(n) = A000203(n) + A274536(n).

%F Dirichlet g.f.: 7*zeta(s-1)*zeta(s). - (After _Ilya Gutkovskiy_)

%p with(numtheory): seq(7*sigma(n), n=1..64);

%t 7*DivisorSigma[1,Range[70]] (* _Harvey P. Dale_, Mar 14 2020 *)

%o (PARI) a(n) = 7 * sigma(n);

%o (GAP) List([1..70],n->7*Sigma(n)); # _Muniru A Asiru_, Sep 28 2018

%Y k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, A274536, this sequence, A319528.

%Y Cf. A216606, A237593.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Sep 22 2018