cp's OEIS Frontend

A269839 Integers k such that the sum of the first k cubes (A000537) is the sum of 2 positive cubes.

%I A269839 #27 Jun 30 2025 10:17:51
%S A269839 2,49,4557,13689,18816,86015,159249,226981,1368912,2112278,25153757,
%T A269839 85184000
%N A269839 Integers k such that the sum of the first k cubes (A000537) is the sum of 2 positive cubes.
%C A269839 In other words, integers k such that (1+2+3+...+k)^2 = x^3 + y^3 where x and y are positive integers, is soluble.
%e A269839 49 is a term because A000537(49) = 1^3 + 2^3 + ... + 48^3 + 49^3 = 1500625 = 70^3 + 105^3.
%e A269839 4557 is a term because A000537(4557) = 1^3 + 2^3 + ... + 4556^3 + 4557^3 = 107856595472409 = 11620^3 + 47369^3.
%o A269839 (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
%o A269839 for(n=0, 1e7, if(isA003325((n*(n+1)/2)^2), print1(n, ", ")));
%Y A269839 Cf. A000537, A003325.
%K A269839 nonn,more
%O A269839 1,1
%A A269839 _Altug Alkan_, Mar 06 2016
%E A269839 a(6)-a(10) from _Chai Wah Wu_, Mar 08 2016
%E A269839 a(11)-a(12) from _Chai Wah Wu_, Jun 30 2025