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%I #49 Dec 31 2020 11:11:15
%S 6,18,24,42,36,72,48,90,78,108,72,168,84,144,144,186,108,234,120,252,
%T 192,216,144,360,186,252,240,336,180,432,192,378,288,324,288,546,228,
%U 360,336,540,252,576,264,504,468,432,288,744,342,558,432,588,324,720,432,720,480,540,360,1008,372,576,624,762
%N a(n) = 6 * sigma(n).
%C 6 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 60-degree-three-dimensional sector arises after the 60-degree-zig-zag folding of every row of the diagram of the isosceles triangle A237593. The top of the pyramid is a six-pointed star formed by six rhombuses (see Links section).
%H Antti Karttunen, <a href="/A274536/b274536.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 60-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) = 6*A000203(n) = 3*A074400(n) = 2*A272027(n).
%F a(n) = A000203(n) + A274535(n) = A074400(n) + A239050(n).
%F Dirichlet g.f.: 6*zeta(s-1)*zeta(s). - _Ilya Gutkovskiy_, Jul 04 2016
%F Conjecture: a(n) = sigma(5*n) = A283118(n) iff n is not a multiple of 5. - _Omar E. Pol_, Oct 02 2018
%p with(numtheory): seq(6*sigma(n), n=1..64);
%t 6DivisorSigma[1, Range[50]] (* _Alonso del Arte_, Jul 04 2016 *)
%o (PARI) a(n) = 6 * sigma(n);
%Y k times sigma(n), k=1..8: A000203, A074400, A272027, A239050, A274535, this sequence, A319527, A319528.
%Y Cf. A237593, A283118.
%K nonn,easy
%O 1,1
%A _Omar E. Pol_, Jun 29 2016
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