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A319528 a(n) = 8 * sigma(n).

%I A319528 #33 Jul 11 2021 02:16:28
%S A319528 8,24,32,56,48,96,64,120,104,144,96,224,112,192,192,248,144,312,160,
%T A319528 336,256,288,192,480,248,336,320,448,240,576,256,504,384,432,384,728,
%U A319528 304,480,448,720,336,768,352,672,624,576,384,992,456,744,576,784,432,960,576,960,640,720,480,1344,496,768,832
%N A319528 a(n) = 8 * sigma(n).
%C A319528 8 times the sum of the divisors of n.
%C A319528 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 45-degree three-dimensional sector arises after the 45-degree zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is an eight-pointed star formed by eight rhombuses (see Links section).
%H A319528 Muniru A Asiru, <a href="/A319528/b319528.txt">Table of n, a(n) for n = 1..10000</a>
%H A319528 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Diagram of the triangle A237593 before the 45-degree-zig-zag folding (rows: 1..28)</a>
%H A319528 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A319528 a(n) = 8*A000203(n) = 4*A074400(n) = 2*A239050(n).
%F A319528 a(n) = A000203(n) + A319527(n).
%F A319528 Dirichlet g.f.: 8*zeta(s-1)*zeta(s). (After _Ilya Gutkovskiy_)
%F A319528 Conjecture: a(n) = sigma(7*n) = A283078(n) iff n is not a multiple of 7.
%F A319528 Conjecture is true, since sigma is multiplicative, so if (7,n) = 1 then sigma(7*n) = sigma(7)*sigma(n) = 8*sigma(n). - _Charlie Neder_, Oct 02 2018
%p A319528 with(numtheory): seq(8*sigma(n), n=1..64);
%t A319528 8*DivisorSigma[1,Range[70]] (* _Harvey P. Dale_, Dec 24 2018 *)
%o A319528 (PARI) a(n) = 8 * sigma(n);
%o A319528 (GAP) List([1..70],n->8*Sigma(n)); # _Muniru A Asiru_, Sep 28 2018
%Y A319528 k times sigma(n), k=1..7: A000203, A074400, A272027, A239050, A274535, A274536, A319527.
%Y A319528 Cf. A008589, A047304, A237593, A283078.
%K A319528 nonn,easy
%O A319528 1,1
%A A319528 _Omar E. Pol_, Sep 22 2018