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A303972
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Total volume of all cubes with side length n which can be split such that n = p + q, p divides q and p < q.
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1
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0, 0, 27, 64, 125, 432, 343, 1024, 1458, 2000, 1331, 6912, 2197, 5488, 10125, 12288, 4913, 23328, 6859, 32000, 27783, 21296, 12167, 82944, 31250, 35152, 59049, 87808, 24389, 162000, 29791, 131072, 107811, 78608, 128625, 326592, 50653, 109744, 177957, 384000
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = n^3 * Sum_{i=1..floor((n-1)/2)} floor((n-i)/i) - floor((n-i-1)/i).
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MAPLE
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v := 0 ;
for p from 1 to n/2 do
q := n-p ;
if p < q and modp(q, p) = 0 then
v := v+n^3 ;
end if;
end do:
v ;
end proc:
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MATHEMATICA
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Table[n^3*Sum[(Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 50}]
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PROG
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(Magma) [0, 0] cat [&+[(((n-k) div k)-(n-k-1) div k)*n^3: k in [1..(n-1) div 2]]: n in [3..80]]; // Vincenzo Librandi, May 04 2018
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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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