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 A270544 Number of ordered pairs (i,j) with |i|, |j| <= n, |i * j| <= n, and i odd. 1

%I

%S 0,6,10,20,24,34,42,52,56,70,78,88,96,106,114,132,136,146,158,168,176,

%T 194,202,212,220,234,242,260,268,278,294,304,308,326,334,352,364,374,

%U 382,400,408,418,434,444,452,478,486,496,504,518,530,548,556,566,582,600

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

%F a(n) = 2*floor((n+1)/2) + 4*Sum_{k=0..floor((n+1)/2)-1}floor(n/(2k+1)).

%F a(n) = A226355(n) - A270543(n).

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

%e a(1) = 6 from (i,j) = (-1,+-1), (1,+-1), (+-1,0).

%e a(2) = 10: (-1,+-2), (-1,+-1), (+-1,0), (1, +-2), (1,+-1).

%t a[n_] := 2 Floor[(n+1)/2] + 4 Sum[Floor[n/(2k+1)], {k,0,Floor[(n+1)/2]-1}]

%o (PARI) a(n) = {my(nb = 0); for(i=-n, n, if ((i % 2), for(j=-n, n, if (abs(i*j) <= n, nb++);););); nb;} \\ _Michel Marcus_, Apr 10 2016

%Y The corresponding sequence where i is even is A270543.

%K nonn

%O 0,2

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

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Last modified February 3 02:45 EST 2023. Contains 360024 sequences. (Running on oeis4.)