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A226323 Number of ordered pairs (i,j) with |i| * |j| <= n and gcd(i,j) <= 1. 1

%I #14 Aug 02 2019 03:24:42

%S 1,9,17,25,33,41,57,65,73,81,97,105,121,129,145,161,169,177,193,201,

%T 217,233,249,257,273,281,297,305,321,329,361,369,377,393,409,425,441,

%U 449,465,481,497,505,537,545,561,577,593,601,617,625,641,657,673,681,697

%N Number of ordered pairs (i,j) with |i| * |j| <= n and gcd(i,j) <= 1.

%C Note that gcd(0,m) = m for any m.

%H Alois P. Heinz, <a href="/A226323/b226323.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 4*A064608(n) + 5 for n > 0, a(0)=1. - _Alois P. Heinz_, Jun 03 2013

%p with(numtheory):

%p a:= n-> `if`(n=0, 1, 5+4*add(mobius(k)^2*floor(n/k), k=1..n)):

%p seq(a(n), n=0..100); # _Alois P. Heinz_, Jun 03 2013

%t f[n_] := Length[Complement[Union[Flatten[Table[If[Abs[i]*Abs[j] ≤ n && GCD[i, j] ≤ 1, {i, j}], {i, -n, n}, {j, -n, n}], 1]], {Null}]]; Table[f[n], {n, 0, 100}]

%Y Cf. A064608, A100449.

%K nonn

%O 0,2

%A _Robert Price_, Jun 03 2013

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Last modified May 18 19:36 EDT 2024. Contains 372666 sequences. (Running on oeis4.)