cp's OEIS Frontend

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

%I A270739 #13 Mar 29 2016 23:41:54
%S A270739 8,25,32,125,128,169,289,512,625,841,1369,1681,2048,2197,2809,3125,
%T A270739 3721,4913,5329,7921,8192,9409,10201,11881,12769,15625,18769,22201,
%U A270739 24389,24649,28561,29929,32761,32768,37249,38809,50653,52441,54289,58081,66049,68921,72361,76729,78125,78961,83521
%N A270739 Prime powers (p^k, p prime, k > 1) of the form x^2 + y^2 where x and y are nonzero integers.
%C A270739 Subsequence of A266927.
%C A270739 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 A270739 125 is a term because 125 = 5^3 = 5^2 + 10^2.
%e A270739 169 is a term because 169 = 13^2 = 5^2 + 12^2.
%e A270739 512 is a term because 512 = 2^9 = 16^2 + 16^2.
%o A270739 (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 A270739 forcomposite(n=4, 1e5, if(isprimepower(n) && isA000404(n), print1(n, ", ")));
%Y A270739 Cf. A000404, A000961, A266927.
%K A270739 nonn
%O A270739 1,1
%A A270739 _Altug Alkan_, Mar 22 2016