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 A002479 Numbers of form x^2 + 2y^2. (Formerly M0547 N0197) 25

%I M0547 N0197

%S 0,1,2,3,4,6,8,9,11,12,16,17,18,19,22,24,25,27,32,33,34,36,38,41,43,

%T 44,48,49,50,51,54,57,59,64,66,67,68,72,73,75,76,81,82,83,86,88,89,96,

%U 97,98,99,100,102,107,108,113,114,118,121,123,128,129,131

%N Numbers of form x^2 + 2y^2.

%C n belongs to this sequence iff every prime p == 5,7 mod 8 dividing n occurs to an even power. - Sharon Sela (sharonsela(AT)hotmail.com), Mar 23 2002

%D L. Euler, (E388) Vollstaendige Anleitung zur Algebra, Zweiter Theil, reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 1, p. 421.

%D D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 59.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002479/b002479.txt">Table of n, a(n) for n = 1..1000</a>

%H L. Euler, <a href="http://www.mathematik.uni-bielefeld.de/~sieben/euler/euler_2.djvu">Vollstaendige Anleitung zur Algebra, Zweiter Teil</a>.

%t q=16; imax=q^2; Select[Union[Flatten[Table[x^2 + 2*y^2, {y,0,q/Sqrt[2]}, {x,0,q}]]], #<=imax&] (* From Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)

%o (PARI) is(n)=my(f=factor(n));for(i=1,#f[,1],if(f[i,1]%8>4 && f[i,2]%2, return(0)));1 \\ _Charles R Greathouse IV_, Nov 20 2012

%Y Cf. A035251.

%Y Complement of A097700.

%K easy,nonn,nice

%O 1,3

%A _N. J. A. Sloane_.

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