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Prime powers (p^k, p prime, k > 1) of the form x^2 + y^2 where x and y are nonzero integers.
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%I #13 Mar 29 2016 23:41:54

%S 8,25,32,125,128,169,289,512,625,841,1369,1681,2048,2197,2809,3125,

%T 3721,4913,5329,7921,8192,9409,10201,11881,12769,15625,18769,22201,

%U 24389,24649,28561,29929,32761,32768,37249,38809,50653,52441,54289,58081,66049,68921,72361,76729,78125,78961,83521

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

%C Subsequence of A266927.

%C 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

%e 125 is a term because 125 = 5^3 = 5^2 + 10^2.

%e 169 is a term because 169 = 13^2 = 5^2 + 12^2.

%e 512 is a term because 512 = 2^9 = 16^2 + 16^2.

%o (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))}

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

%Y Cf. A000404, A000961, A266927.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 22 2016