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A084349 Squarefree numbers that are not the sum of two squares.

%I A084349 #23 Dec 02 2015 12:05:57
%S A084349 1,3,6,7,11,14,15,19,21,22,23,30,31,33,35,38,39,42,43,46,47,51,55,57,
%T A084349 59,62,66,67,69,70,71,77,78,79,83,86,87,91,93,94,95,102,103,105,107,
%U A084349 110,111,114,115,118,119,123,127,129,131,133,134,138,139,141,142,143
%N A084349 Squarefree numbers that are not the sum of two squares.
%C A084349 Intersection of A005117 (squarefree) and A018825. - _Michel Marcus_, Dec 02 2015
%H A084349 Reinhard Zumkeller, <a href="/A084349/b084349.txt">Table of n, a(n) for n = 1..10000</a>
%H A084349 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A084349 A005117(10) = 14: 14 - 1^2 = 13, 14 - 2^2 = 10 and 14 - 3^3 = 5 are nonsquares, therefore 14 is a term;
%e A084349 A005117(9) = 13 is not a term: A020893(4) = 13 = 2^2 + 3^2.
%t A084349 Prepend[Select[Range@ 144, SquareFreeQ@ # && SquaresR[2, #] == 0 &], 1] (* _Michael De Vlieger_, Dec 02 2015 *)
%o A084349 (Haskell)
%o A084349 a084349 n = a084349_list !! (n-1)
%o A084349 a084349_list = 1 : filter (\x -> all (== 0) $ map (a010052 . (x -)) $
%o A084349                            takeWhile (<= x) a000290_list) a005117_list
%o A084349 -- _Reinhard Zumkeller_, Dec 11 2011
%Y A084349 Cf. A000290, A005117, A010052, A018825, A020893.
%K A084349 nonn
%O A084349 1,2
%A A084349 _Reinhard Zumkeller_, Jun 21 2003