%I A034836
%S A034836 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,6,2,2,3,4,1,5,1,5,2,2,2,
%T A034836 8,1,2,2,6,1,5,1,4,4,2,1,9,2,4,2,4,1,6,2,6,2,2,1,10,1,2,4,7,2,5,1,4,2,
%U A034836 5,1,12,1,2,4,4,2,5,1,9,4,2,1,10,2,2,2,6,1,10,2,4,2,2,2,12,1,4,4,8
%N A034836 Number of ways to write n as n = x*y*z with 1<=x<=y<=z<=n.
%C A034836 Number of boxes with integer edge lengths and volume n.
%C A034836 Starts the same as, but is different from, A033273. First values of n 
               such that a(n) differs from A033273(n) are 36,48,60,64,72,80,84,90,
               96,100 - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 25 2002
%e A034836 a(12)=4 because we can write 12=1*1*12=1*2*6=1*3*4=2*2*3
%p A034836 f:=proc(n) local t1,i,j,k; t1:=0; for i from 1 to n do for j from i to 
               n do for k from j to n do if i*j*k = n then t1:=t1+1; fi; od: od: 
               od: t1; end;
%o A034836 (PARI) A038548(n)=if(n>=0, sumdiv(n, d, d*d<=n)) /* <== rhs from A038548 
               (Michael Somos) */ a(n)=if(n>=0, sumdiv(n, d, if(d^3<=n, A038548(n/
               d) - sumdiv(n/d, d0, d0<d)))) - Rick L. Shepherd (rshepherd2(AT)hotmail.com), 
               Aug 27 2006
%Y A034836 See also: writing n = x*y (A038548, unordered, A000005, ordered), n = 
               x*y*z (this sequence, unordered, A007425, ordered), n = w*x*y*z (A007426, 
               ordered)
%Y A034836 Cf. A088432, A088433, A088434.
%Y A034836 Sequence in context: A069157 A076526 A033273 this_sequence A001055 A129138 
               A112970
%Y A034836 Adjacent sequences: A034833 A034834 A034835 this_sequence A034837 A034838 
               A034839
%K A034836 nonn
%O A034836 1,4
%A A034836 Erich Friedman (erich.friedman(AT)stetson.edu)