Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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