OFFSET
1,3
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} i^2 * (n-i) * (floor((n-i)/i) - floor((n-i-1)/i)).
EXAMPLE
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.
MAPLE
A303973 := proc(n)
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:
seq(A303973(n), n=1..40) ; # R. J. Mathar, Jun 25 2018
MATHEMATICA
Table[Sum[i^2 (n - i) (Floor[(n - i)/i] - Floor[(n - i - 1)/i]), {i, Floor[(n - 1)/2]}], {n, 100}]
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, May 03 2018
STATUS
approved