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A267119
Noncube integers n such that n^2 + 1 is the sum of 2 positive cubes.
1
995, 1191, 1608, 2049, 3988, 4584, 4818, 6323, 12811, 14642, 14806, 16710, 27400, 27672, 28881, 38501, 39192, 44892, 46401, 46818, 53438, 63455, 64086, 65385, 72800, 81711, 98146, 114729, 126624, 142345, 159013, 161573, 169358, 184644, 186363, 197559, 200024, 203432, 211307
OFFSET
1,1
COMMENTS
Corresponding values of n^2 + 1 are 990026, 1418482, 2585665, 4198402, 15904145, 21013057, 23213125, ...
Prime terms of this sequence are 6323, 38501, 159013, 161573, ...
Sequence focuses on the noncube values of n in order to eliminate trivial solutions of motivation equation that is n^2 + 1 = x^3 + y^3 where x and y are positive integers.
Union of this sequence and all positive cubes give the integers n such that n^2 + 1 are the sum of 2 positive cubes.
LINKS
EXAMPLE
995 is a term because 995^2 + 1 = 990026 = 51^3 + 95^3.
1191 is a term because 1191^2 + 1 = 1418482 = 85^3 + 93^3.
1608 is a term because 1608^2 + 1 = 2585665 = 76^3 + 129^3.
PROG
(PARI) T = thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=2, 200000, if(is(n^2+1) && ispower(n, 3) == 0, print1(n, ", ")))
CROSSREFS
Sequence in context: A035857 A028513 A373105 * A210315 A182694 A234847
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 10 2016
STATUS
approved