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

7688, 70688, 95048, 120125, 131072, 186003, 219488, 219501, 265837, 286443, 304175, 371293, 412232, 464648, 465125, 596183, 628864, 699867, 729632, 732736, 834632, 860672, 1104500, 1119371, 1162213, 1173512, 1257728, 1290496, 1318707, 1431125, 1438208, 1472207, 1527752, 1597696, 1601613

Offset: 1

Author

Robert Israel, Mar 26 2019

Keywords

• nonn

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).

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..468

Crossrefs

Cf. A216427.

Programs

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;