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 A267416 Perfect powers of the form x^3 + y^3 where x and y are distinct positive integers. 1
 9, 243, 576, 6561, 9604, 28224, 36864, 51984, 97344, 140625, 177147, 275625, 345744, 419904, 450241, 614656, 717409, 1028196, 1058841, 1399489, 1500625, 1590121, 1750329, 1806336, 2359296, 3326976, 4782969, 6230016, 7001316, 7962624, 8340544, 9000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A267088. Intersection of A001597 and A024670. Obviously, because of Fermat's Last Theorem, a(n) cannot be a cube. Corresponding exponents are 2, 5, 2, 8, 2, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 4, 2, ... Motivation for this sequence is the equation m^k = x^3 + y^3 where m > 0, k >= 2 and x, y are distinct positive integers. LINKS Chai Wah Wu, Table of n, a(n) for n = 1..4707 EXAMPLE 9 is a term because 9 = 3^2 = 1^3 + 2^3. 243 is a term because 243 = 3^5 = 3^3 + 6^3. 576 is a term because 576 = 24^2 = 4^3 + 8^3. 51984 is a term because 51984 = 228^2 = 11^3 + 37^3. MATHEMATICA Union@ Select[Plus @@@ Union@ Map[Sort, Permutations[Range^3, {2}]], # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* Michael De Vlieger, Jan 15 2016, after Ant King at A001597 *) PROG (PARI) is(n) = for( i=ceil(sqrtn(n\2+1, 3)), sqrtn(n-.5, 3), ispower(n-i^3, 3) & return(1)); for(n=1, 1e7, if(is(n) && ispower(n), print1(n, ", "))); CROSSREFS Cf. A001597, A024670, A267088. Sequence in context: A183903 A251670 A075127 * A268088 A285511 A013733 Adjacent sequences:  A267413 A267414 A267415 * A267417 A267418 A267419 KEYWORD nonn AUTHOR Altug Alkan, Jan 14 2016 STATUS approved

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Last modified November 13 23:01 EST 2019. Contains 329106 sequences. (Running on oeis4.)