A355813 - OEIS

%I #11 Jul 18 2022 22:49:42

%S 1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,3,2,2,

%T 1,2,2,2,4,1,2,4,2,2,3,2,2,2,2,2,2,4,3,2,2,4,2,1,2,2,6,2,2,4,3,2,1,2,

%U 2,2,2,2,2,2,3,4,4,2,2,1,2,6,1,2,6,4,2,4,1,2,2,8

%N Number of solutions (p,q) to 1/s^2 + 1/t^2 = 1/p^2 + 1/q^2 where p,q < t = A355812(n).

%H Jianing Song, <a href="/A355813/b355813.txt">Table of n, a(n) for n = 1..307</a>

%e A355812(1) = 35. 1/s^2 + 1/35^2 = 1/p^2 + 1/q^2 has one solution, (s,p,q) = (5,7,7), so a(1) = 35.

%e A355812(2) = 55. 1/s^2 + 1/55^2 = 1/p^2 + 1/q^2 has two solutions, (s,p,q) = (10,11,22) and (10,22,11), so a(2) = 55.

%e A355812(32) = 210. 1/s^2 + 1/210^2 = 1/p^2 + 1/q^2 has three solutions, (s,p,q) = (30,42,42), (95,114,133) and (95,133,114), so a(32) = 3.

%o (PARI) b(n) = my(v=[;],r); for(p=1, n-1, for(q=1, n-1, r=1/(1/p^2+1/q^2-1/n^2); if(r==r\1 && issquare(r), v=concat(v,[p;q])))); v

%o list(lim) = my(v=[],num); for(n=1, lim, if((num=#b(n))>0, v=concat(v, num))); v

%Y Cf. A355812, A355814.

%K nonn

%O 1,2

%A _Jianing Song_, Jul 18 2022