OFFSET
1,1
COMMENTS
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.
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).
LINKS
Robert Israel, Table of n, a(n) for n = 1..468
EXAMPLE
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.
MAPLE
N:= 10^6: # to get terms <= N
A23:= {seq(seq(x^2*y^3, x= 2.. floor(sqrt(N/abs(y)^3))), y=2..floor(N^(1/3)))}: n:=nops(A23):
Res:= NULL:
for k from 1 to n do
z:= A23[k];
for i from 1 to n do
x:= A23[i];
if 2*x > z then break fi;
if member(z-x, A23) and igcd(z, x)=1 then Res:= Res, z; break fi
od od:
Res;
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 26 2019
STATUS
approved