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Integers n such that the sum of the first n cubes (A000537) is the sum of 2 positive cubes.
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%I #20 Mar 09 2016 03:08:43

%S 2,49,4557,13689,18816,86015,159249,226981,1368912,2112278

%N Integers n such that the sum of the first n cubes (A000537) is the sum of 2 positive cubes.

%C In other words, integers n such that (1+2+3+...+n)^2 = x^3 + y^3 where x and y are positive integers, is soluble.

%e 49 is a term because A000537(49) = 1^3 + 2^3 + ... + 48^3 + 49^3 = 1500625 = 70^3 + 105^3.

%e 4557 is a term because A000537(4557) = 1^3 + 2^3 + ... + 4556^3 + 4557^3 = 107856595472409 = 11620^3 + 47369^3.

%o (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));

%o for(n=0, 1e7, if(isA003325((n*(n+1)/2)^2), print1(n, ", ")));

%Y Cf. A000537, A003325.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Mar 06 2016

%E a(6)-a(10) from _Chai Wah Wu_, Mar 08 2016