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A303973
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Total volume of all rectangular prisms with dimensions (p,p,q) such that n = p + q, p divides q and p < q.
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1
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0, 0, 2, 3, 4, 21, 6, 31, 62, 41, 10, 260, 12, 61, 372, 263, 16, 648, 18, 722, 868, 101, 22, 2292, 524, 121, 1700, 1544, 28, 3873, 30, 2135, 2964, 161, 2156, 7703, 36, 181, 4756, 6690, 40, 9051, 42, 4844, 11088, 221, 46, 18788, 2106, 5366, 10308, 7610, 52
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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) = Sum_{i=1..floor((n-1)/2)} i^2 * (n-i) * (floor((n-i)/i) - floor((n-i-1)/i)).
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EXAMPLE
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For n =12 the prism (p,p,q) = (1,1,11) contributes 1*1*11=11 to the volume, (2,2,10) contributes 2*2*10= 40, (3,3,9) contributes 3*3*9= 81, (4,4,8) contributes 128. The total is a(12) = 11+40+81+128 = 260.
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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+p^2*q ;
end if;
end do:
v ;
end proc:
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MATHEMATICA
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Table[Sum[i^2 (n - i) (Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 100}]
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PROG
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(Magma) [0, 0] cat [&+[k^2*(n-k)*(((n-k) div k)-((n-k-1) div k)): 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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