A226355 - OEIS

%I #18 Jan 11 2017 02:35:55

%S 1,9,21,33,49,61,81,93,113,129,149,161,189,201,221,241,265,277,305,

%T 317,345,365,385,397,433,449,469,489,517,529,565,577,605,625,645,665,

%U 705,717,737,757,793,805,841,853,881,909,929,941,985,1001,1029,1049,1077,1089,1125,1145,1181

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

%H Robert Price and Charles R Greathouse IV, <a href="/A226355/b226355.txt">Table of n, a(n) for n = 0..10000</a> (first 400 terms from Price)

%F a(n) = 1 + 4n + 4*Sum_{k=1..n} tau(k), where tau(k) is the number of divisors of k. - _Lorenz H. Menke, Jr._, Mar 15 2016

%p with(numtheory): A226355:=n->1+4*n+4*add(tau(k), k=1..n): seq(A226355(n), n=0..100); # _Wesley Ivan Hurt_, Jan 10 2017

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

%t f[n_]:=4 Sum[Length[Divisors[k]], {k, 1, n}] + 4 n + 1 (* _Lorenz H. Menke, Jr._, Mar 15 2016 *)

%o (PARI) a(n) = 8*sum(k=1, sqrtint(n), n\k) - 4*sqrtint(n)^2 + 4*n + 1 \\ _Charles R Greathouse IV_, Mar 16 2016

%K nonn

%O 0,2

%A _Robert Price_, Jun 04 2013