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

0, 6, 10, 20, 24, 34, 42, 52, 56, 70, 78, 88, 96, 106, 114, 132, 136, 146, 158, 168, 176, 194, 202, 212, 220, 234, 242, 260, 268, 278, 294, 304, 308, 326, 334, 352, 364, 374, 382, 400, 408, 418, 434, 444, 452, 478, 486, 496, 504, 518, 530, 548, 556, 566, 582, 600

Offset

0,2

Links

Table of n, a(n) for n=0..55.

Formula

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

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

Example

a(0) = 0 from (i,j) = ().
a(1) = 6 from (i,j) = (-1,+-1), (1,+-1), (+-1,0).
a(2) = 10: (-1,+-2), (-1,+-1), (+-1,0), (1, +-2), (1,+-1).

Mathematica

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

Prog

(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

Crossrefs

The corresponding sequence where i is even is A270543.

Sequence in context: A356055 A300020 A068017 * A181995 A169810 A095146

Adjacent sequences: A270541 A270542 A270543 * A270545 A270546 A270547

Keyword

nonn

Author

Lorenz H. Menke, Jr., Mar 18 2016

Status

approved