A274247 - OEIS

%I #9 Jun 29 2016 00:05:17

%S 12348,16464,433664,444528,617400,790272,1053696,2534400,2737152,

%T 6585600,6667920,7024032

%N Numbers n such that n^k is the sum of a positive square and a positive cube for all k not divisible by 6.

%C It is sufficient to prove that the decomposition exists for k=1..5, because if n^k = a^2+b^3, then n^(k+6) = (n^3*a)^2 + (n^2*b)^3.

%e 12348 is a term since 12348 = 98^2 + 14^3, 12348^2 = 9604^2 + 392^3, 12348^3 = 1361367^2 + 3087^3, 12348^4 = 76236552^2 + 259308^3, 12348^5 = 11206773144^2 + 5445468^3.

%o (PARI) isA055394(n) = for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1)));0

%o isok(n) = isA055394(n) && isA055394(n^2) && isA055394(n^3) && isA055394(n^4) && isA055394(n^5)

%Y Cf. A055394.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Jun 16 2016

%E a(6)-a(12) from _Giovanni Resta_, Jun 18 2016