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

1,1

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

Cf. A216427.

Sequence in context: A012082 A184026 A035907 * A183974 A234223 A253923

Adjacent sequences: A307131 A307132 A307133 * A307135 A307136 A307137

Keyword

nonn

Author

Robert Israel, Mar 26 2019

Status

approved