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A319528
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a(n) = 8 * sigma(n).
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10
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8, 24, 32, 56, 48, 96, 64, 120, 104, 144, 96, 224, 112, 192, 192, 248, 144, 312, 160, 336, 256, 288, 192, 480, 248, 336, 320, 448, 240, 576, 256, 504, 384, 432, 384, 728, 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
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OFFSET
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1,1
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COMMENTS
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8 times the sum of the divisors of n.
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 a eight-pointed star formed by eight rhombuses (see Links section).
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LINKS
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Muniru A Asiru, Table of n, a(n) for n = 1..10000
Omar E. Pol, Diagram of the triangle A237593 before the 45-degree-zig-zag folding (rows: 1..28)
Index entries for sequences related to sigma(n)
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FORMULA
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a(n) = 8*A000203(n) = 4*A074400(n) = 2*A239050(n).
a(n) = A000203(n) + A319527(n).
Dirichlet g.f.: 8*zeta(s-1)*zeta(s). - (After Ilya Gutkovskiy)
Conjecture: a(n) = sigma(7*n) = A283078(n) iff n is not a multiple of 7.
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
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MAPLE
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with(numtheory): seq(8*sigma(n), n=1..64);
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MATHEMATICA
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8*DivisorSigma[1, Range[70]] (* Harvey P. Dale, Dec 24 2018 *)
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PROG
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(PARI) a(n) = 8 * sigma(n);
(GAP) List([1..70], n->8*Sigma(n)); # Muniru A Asiru, Sep 28 2018
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CROSSREFS
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k times sigma(n), k=1..7: A000203, A074400, A272027, A239050, A274535, A274536, A319527.
Cf. A008589, A047304, A237593, A283078.
Sequence in context: A333427 A128690 A283078 * A140403 A108578 A305241
Adjacent sequences: A319525 A319526 A319527 * A319529 A319530 A319531
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KEYWORD
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nonn,easy
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AUTHOR
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Omar E. Pol, Sep 22 2018
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STATUS
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approved
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