|
%I #9 Nov 07 2018 21:46:45
%S 0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0
%N Number of ways 1/n can be written as 1/x^2 + 1/y^2 with y >= x >= 1.
%C Number of ordered pairs (x,y), with n = (x^2)(y^2)/(x^2 + y^2) and y >= x > 0. - _Antti Karttunen_, Nov 07 2018
%H Antti Karttunen, <a href="/A063665/b063665.txt">Table of n, a(n) for n = 1..100000</a>
%e a(90)=1 since 1/90 = 1/10^2 + 1/30^2
%e a(98)=2 since 1/98 = 1/10^2 + 1/70^2 = 1/14^2 + 1/14^2.
%e a(14400) = 3 since 1/14400 = 1/130^2 + 1/312^2 = 1/136^2 + 1/255^2 = 1/150^2 + 1/200^2. - _Antti Karttunen_, Nov 07 2018
%o (PARI) A063665(n) = { my(s=0); for(x=1,n,for(y=x,n,if((n*(x*x+y*y)) == (x*x*y*y), s++))); (s); }; \\ _Antti Karttunen_, Nov 07 2018
%o (PARI) A063665(n) = { my(s=0,y); for(x=sqrtint(n),n,my(x2=x*x); if((x2>n)&&issquare((n*x2)/(x2-n),&y)&&(1==denominator(y))&&(y>=x),s++)); (s); }; \\ _Antti Karttunen_, Nov 07 2018
%Y Cf. A000161, A025426, A018892, A063664.
%K nonn
%O 1,98
%A _Henry Bottomley_, Jul 25 2001
%E Definition clarified by _Antti Karttunen_, Nov 07 2018
|
