A274247 Numbers n such that n^k is the sum of a positive square and a positive cube for all k not divisible by 6.

12348, 16464, 433664, 444528, 617400, 790272, 1053696, 2534400, 2737152, 6585600, 6667920, 7024032

Offset: 1

Author

Altug Alkan, Jun 16 2016

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A055394.

Programs

PARI

isA055394(n) = for(k=1, sqrtnint(n-1, 3), if(issquare(n-k^3), return(1)));0
isok(n) = isA055394(n) && isA055394(n^2) && isA055394(n^3) && isA055394(n^4) && isA055394(n^5)

Extensions

a(6)-a(12) from Giovanni Resta, Jun 18 2016