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A307134 Terms of A216427 that are the sum of two coprime terms of A216427. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Robert Israel, Mar 26 2019
STATUS
approved

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Last modified February 25 13:12 EST 2024. Contains 370330 sequences. (Running on oeis4.)