A071694 Number of ways to write n as n = x*y*z/(x+y+z) 1 <= x <= y <= z <= n.

0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 3, 1, 3, 5, 3, 2, 3, 2, 7, 5, 1, 3, 8, 2, 4, 8, 4, 3, 5, 2, 9, 5, 2, 14, 12, 1, 4, 10, 10, 3, 5, 2, 11, 11, 2, 4, 13, 5, 10, 8, 6, 3, 14, 12, 22, 5, 1, 5, 14, 1, 5, 22, 11, 13, 11, 2, 11, 9, 6, 5, 19, 1, 5, 19, 10, 13, 6, 4, 33, 14, 1, 5, 24, 6, 6, 11, 10, 5

Offset: 1

Author

Benoit Cloitre, Jun 23 2002

Keywords

• nonn

Comments

If n is a prime other than 3, then a(n) = A000005(n+1)/2 - 1. - Robert Israel, Oct 29 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A063520.

Programs

Maple

f:= proc(n) local x,y,z,t;
t:= 0;
  for x from 1 to n do
    for y from max(x,ceil(n/x)) to n do
      if x*y = n then next fi;
      z:= n*(x+y)/(x*y-n);
      if z::integer and z>=y and z<=n then t:= t+1 fi
od od:
t
end proc:
map(f, [$1..100]); # Robert Israel, Oct 29 2018

Mathematica

a[n_] := Sum[Boole[x y z/(x + y + z) == n], {x, n}, {y, x}, {z, y}];
Array[a, 100] (* Jean-François Alcover, Aug 24 2020 *)

PARI

for(n=1,90,print1(sum(a=1,n,sum(b=1,a,sum(c=1,b,if(a*b*c/(a+b+c)-n,0,1)))),","))