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Perfect squares which can be written neither as a^2+b^2, nor as a^2+2*b^2, nor as a^2+3*b^2, nor as a^2+7*b^2, with a > 0 and b > 0.
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%I #15 Sep 19 2012 18:13:23

%S 1,2209,27889,96721,146689,229441,253009,418609,516961,703921,786769,

%T 966289,1324801,1495729,1739761,2211169,2283121,2430481,3323329,

%U 3411409,4255969,4879681,5527201,5755201,7091569,7219969,8427409,8994001,9138529,10029889,10182481,11282881,11607649,12439729,13476241,14922769,15295921

%N Perfect squares which can be written neither as a^2+b^2, nor as a^2+2*b^2, nor as a^2+3*b^2, nor as a^2+7*b^2, with a > 0 and b > 0.

%C If a composite number C, in case, can be written in the form C = a^2+k*b^2, for some integers a & b, then every prime factor P (for C) being raised to an odd power can be written in the form P = c^2+k*d^2, for some integers c & d.

%C This statement is only true for k = 1, 2, 3.

%C For k = 7, with the exception of the prime factor 2, the statement mentioned above is true.

%Y Cf. A216451, A216500, A216501, A216671, A216679, A216680, A216682

%K nonn

%O 1,2

%A _V. Raman_, Sep 17 2012