A272119 Values of a^2 + b^2 such that the equation (a^2 + b^2)^2 = x^2 + y^2 + z^2 is soluble where a, b, x, y, z are nonzero integers.

13, 17, 18, 25, 26, 29, 34, 37, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 122, 125, 130, 136, 137, 145, 146, 148, 149, 153, 157, 162, 164, 169, 170, 173, 178, 180, 181, 185, 193, 194, 197, 200, 202, 205, 208, 212, 218

Offset: 1

Author

Altug Alkan, Apr 21 2016

Keywords

• nonn
• easy

Comments

52 is the first term that is not a member of A046711.

Examples

			13 is a term because 13 = 2^2 + 3^2 and 13^2 = 3^2 + 4^2 + 12^2.
		

Crossrefs

Cf. A000404, A000408, A046711.

Programs

PARI

isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
isA000408(n) = {my(a, b) ; a=1 ; while(a^2+1A000404(n) && isA000408(n^2), print1(n, ", ")));