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A270739
Prime powers (p^k, p prime, k > 1) of the form x^2 + y^2 where x and y are nonzero integers.
0
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
1,1
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
EXAMPLE
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.
PROG
(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, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 22 2016
STATUS
approved