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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 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

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