A270739 Prime powers (p^k, p prime, k > 1) of the form x^2 + y^2 where x and y are nonzero integers.

8, 25, 32, 125, 128, 169, 289, 512, 625, 841, 1369, 1681, 2048, 2197, 2809, 3125, 3721, 4913, 5329, 7921, 8192, 9409, 10201, 11881, 12769, 15625, 18769, 22201, 24389, 24649, 28561, 29929, 32761, 32768, 37249, 38809, 50653, 52441, 54289, 58081, 66049, 68921, 72361, 76729, 78125, 78961, 83521

Offset: 1

Author

Altug Alkan, Mar 22 2016

Keywords

• nonn

Comments

Subsequence of A266927.

Among the Gaussian integers, these numbers have two distinct prime factors, and four or more prime factors when counted with multiplicity. - Alonso del Arte, Mar 22 2016

Examples

			125 is a term because 125 = 5^3 = 5^2 + 10^2.
169 is a term because 169 = 13^2 = 5^2 + 12^2.
512 is a term because 512 = 2^9 = 16^2 + 16^2.
		

Crossrefs

Cf. A000404, A000961, A266927.

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))}
forcomposite(n=4, 1e5, if(isprimepower(n) && isA000404(n), print1(n, ", ")));