A267416 Perfect powers of the form x^3 + y^3 where x and y are distinct positive integers.
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
Offset: 1
Keywords
Examples
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.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..4707
Programs
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Mathematica
Union@ Select[Plus @@@ Union@ Map[Sort, Permutations[Range[210]^3, {2}]], # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &] (* Michael De Vlieger, Jan 15 2016, after Ant King at A001597 *) -
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, ", ")));
Comments