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A307134 Terms of A216427 that are the sum of two coprime terms of A216427.

%I A307134 #24 May 08 2021 08:28:39
%S A307134 7688,70688,95048,120125,131072,186003,219488,219501,265837,286443,
%T A307134 304175,371293,412232,464648,465125,596183,628864,699867,729632,
%U A307134 732736,834632,860672,1104500,1119371,1162213,1173512,1257728,1290496,1318707,1431125,1438208,1472207,1527752,1597696,1601613
%N A307134 Terms of A216427 that are the sum of two coprime terms of A216427.
%C A307134 It is possible for a term of the sequence to be such a sum in more than one way, e.g., 1119371 = 215168 + 904203 = 366368 + 753003.
%C A307134 There are parametric solutions, and in particular the sequence is infinite. For example, 3^3*(-44100*k^2 - 21140*k + 471)^2 + 5^3*(-26460*k^2 + 4788*k + 865)^2 = 2^3*(132300*k^2 + 8820*k + 3527)^2, and these are coprime unless k==3 (mod 13).
%H A307134 Robert Israel, <a href="/A307134/b307134.txt">Table of n, a(n) for n = 1..468</a>
%e A307134 a(3)=95048 is in the sequence because 95048 = 2^3*109^2 = 45125 + 49923 = 5^3*19^2 + 3^3*43^2, and gcd(45125,49923)=1.
%p A307134 N:= 10^6: # to get terms <= N
%p A307134 A23:= {seq(seq(x^2*y^3, x= 2.. floor(sqrt(N/abs(y)^3))),y=2..floor(N^(1/3)))}: n:=nops(A23):
%p A307134 Res:= NULL:
%p A307134 for k from 1 to n do
%p A307134   z:= A23[k];
%p A307134   for i from 1 to n do
%p A307134     x:= A23[i];
%p A307134     if 2*x > z then break fi;
%p A307134     if member(z-x,A23) and igcd(z,x)=1 then  Res:= Res, z; break fi
%p A307134 od od:
%p A307134 Res;
%Y A307134 Cf. A216427.
%K A307134 nonn
%O A307134 1,1
%A A307134 _Robert Israel_, Mar 26 2019