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 A270543 Number of ordered pairs (i,j) of integers with |i|, |j| <= n, |i * j| <= n, and i even. 1

%I

%S 1,3,11,13,25,27,39,41,57,59,71,73,93,95,107,109,129,131,147,149,169,

%T 171,183,185,213,215,227,229,249,251,271,273,297,299,311,313,341,343,

%U 355,357,385,387,407,409,439,431,443,445,481,483,499,501,521,523,543,545

%N Number of ordered pairs (i,j) of integers with |i|, |j| <= n, |i * j| <= n, and i even.

%F a(n) = 1 + 2*n + 2*floor(n/2) + 4*Sum_{k=1..floor(n/2)}floor(n/(2k)).

%F a(n) = A226355(n) - A270544(n).

%e a(0) = 1 from (i,j) = (0,0).

%e a(1) = 3 from (i,j) = (0,0), (0,1), (0,-1).

%e a(2) = 11: (0,0), (0,+-1), (0,+-2), (+-2, 0), (+-2,+-1).

%t a[n_]:=1+2n+2Floor[n/2]+4Sum[Floor[n/(2k)],{k,1,Floor[n/2]}]

%o (PARI) a(n) = {my(nb = 0); for (i=-n, n, if ((i % 2) == 0, for(j=-n, n, if (abs(i*j) <= n, nb++);););); nb;}

%Y The corresponding sequence where i is odd is A270544.

%Y Cf. A226355.

%K nonn

%O 0,2

%A _Lorenz H. Menke, Jr._, Mar 18 2016

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Last modified December 8 01:51 EST 2022. Contains 358672 sequences. (Running on oeis4.)