|
%I #11 Jun 17 2013 11:57:15
%S 1,2,3,3,4,4,4,6,6,4,6,6,4,8,10,5,6,6,6,12,8,4,8,12,6,8,12,6,8,8,6,12,
%T 8,8,18,9,4,8,16,8,8,8,6,18,12,4,10,15,9,12,12,6,8,16,16,16,8,4,12,12,
%U 4,12,21,14,16,8,6,12,16,8,12,12,4,12,18,12,16,8,10,25,10,4,12,24,8,8
%N Number of solutions (r,s), 0< r< s, to the equation 1/n = 1/r + 1/s + 1/(r*s).
%C Unordered solutions to the equation 1/n = 1/r+1/s+1/(r*s) are r=d+n, s=n*(n+1)/d+n, where d is factor of n*(n+1) not greater than n.
%C Number of divisors of n-th oblong number not greater than n. - Chandler
%H Ray Chandler, <a href="/A063123/b063123.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) = tau(n)*tau(n+1)/2 = A092517(n)/2.
%e a(2)=2 because 1/2=1/3+1/8+1/24=1/4+1/5+1/20.
%o (PARI) a(n) = numdiv(n)*numdiv(n+1)/2 \\ _Michel Marcus_, Jun 17 2013
%Y Cf. A063520.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Aug 08 2001
|
