|
|
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
|
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
|
|
|
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[210]^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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|