A226355 Number of ordered pairs (i,j) with |i| * |j| <= n.

1, 9, 21, 33, 49, 61, 81, 93, 113, 129, 149, 161, 189, 201, 221, 241, 265, 277, 305, 317, 345, 365, 385, 397, 433, 449, 469, 489, 517, 529, 565, 577, 605, 625, 645, 665, 705, 717, 737, 757, 793, 805, 841, 853, 881, 909, 929, 941, 985, 1001, 1029, 1049, 1077, 1089, 1125, 1145, 1181

Offset: 0

Author

Robert Price, Jun 04 2013

Keywords

• nonn

Links

• Robert Price and Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 (first 400 terms from Price)

Programs

Maple

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

Mathematica

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

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

Formula

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