cp's OEIS Frontend

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

%I A071694 #22 Oct 12 2020 03:45:28
%S A071694 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,
%T A071694 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,
%U A071694 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
%N A071694 Number of ways to write n as n = x*y*z/(x+y+z) 1 <= x <= y <= z <= n.
%C A071694 If n is a prime other than 3, then a(n) = A000005(n+1)/2 - 1. - _Robert Israel_, Oct 29 2018
%H A071694 Robert Israel, <a href="/A071694/b071694.txt">Table of n, a(n) for n = 1..1000</a>
%p A071694 f:= proc(n) local x,y,z,t;
%p A071694 t:= 0;
%p A071694   for x from 1 to n do
%p A071694     for y from max(x,ceil(n/x)) to n do
%p A071694       if x*y = n then next fi;
%p A071694       z:= n*(x+y)/(x*y-n);
%p A071694       if z::integer and z>=y and z<=n then t:= t+1 fi
%p A071694 od od:
%p A071694 t
%p A071694 end proc:
%p A071694 map(f, [$1..100]); # _Robert Israel_, Oct 29 2018
%t A071694 a[n_] := Sum[Boole[x y z/(x + y + z) == n], {x, n}, {y, x}, {z, y}];
%t A071694 Array[a, 100] (* _Jean-François Alcover_, Aug 24 2020 *)
%o A071694 (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)))),","))
%Y A071694 Cf. A000005, A063520.
%K A071694 nonn
%O A071694 1,8
%A A071694 _Benoit Cloitre_, Jun 23 2002