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%I #44 Apr 14 2019 14:22:32
%S 3,4,5,10,11,14,18,21,23,25,29,36,38,39,41,44,45,46,47,52,55,57,59,60,
%T 66,73,74,76,77,82,83,93,95,99,100,101,102,109,111,113,116,118,119,
%U 121,122,129,131,137,138,145,146,147,148,149,150,154,155,158,165
%N Positive integers that are not divisible by any cube greater than 1 and cannot be written as the sum of two cubes of rational numbers.
%C This sequence is infinite.
%C This sequence is the complement of (A020897 minus A046099), except 1.
%D W. Sierpiński, 250 Problems in Elementary Number Theory, 1970, page 112.
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/csolve/fermat.pdf">On a Generalized Fermat-Wiles Equation</a> [broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010602030546/http://www.mathsoft.com/asolve/fermat/fermat.html">On a Generalized Fermat-Wiles Equation</a> [From the Wayback Machine]
%H Ernst S. Selmer, <a href="http://dx.doi.org/10.1007/BF02395746">The diophantine equation ax^3 + by^3 + cz^3 = 0</a>, Acta Math. 85 (1951), pp. 203-362.
%e a(4)=10 cannot be written as c^3 + d^3 where both c and d are rational numbers.
%e 22 = (25469/9954)^3 + (17299/9954)^3, so 22 is not in the sequence.
%Y Cf. A003325, A020897, A046099.
%K nonn,more
%O 1,1
%A _Marco Ripà_, Jul 31 2015
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