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A216055 Numbers that are mean of four squares of distinct primes. 0

%I #11 Aug 31 2012 02:12:25

%S 51,63,81,87,91,93,111,117,121,123,129,133,135,139,141,147,151,153,

%T 157,165,169,171,175,177,181,183,189,193,195,199,205,207,211,213,217,

%U 219,223,231,235,237,241,247,249,253,255,259,261,265,267,271,277,279,285

%N Numbers that are mean of four squares of distinct primes.

%C Any four squares of odd primes have integer average.

%C First integers with two and three representations are 111 and 259:

%C 111=(3^2+5^2+7^2+19^2)/4=(3^2+5^2+11^2+17^2)/4,

%C 259=(5^2+7^2+11^2+29^2)/4=(5^2+11^2+19^2+23^2)/4=(7^2+13^2+17^2+23^2)/4.

%C First primes in this sequence are: 139, 151, 157, 181, 193, 199, 211, 223, 241, 271, 277, 307, 331, 337, 349.

%C First squares are:

%C {81, 121, 169, 289, 361, 441, 529, 625, 729, 841, 961, 1089, 1225}=

%C {9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35}^2.

%e 51=(3^2+5^2+7^2+11^2)/4, 63=(3^2+5^2+7^2+13^2)/4.

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 30 2012

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