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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 an eight-pointed star formed by eight rhombuses (see Links section).
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LINKS
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FORMULA
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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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PROG
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(PARI) a(n) = 8 * sigma(n);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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