A270543 Number of ordered pairs (i,j) of integers with |i|, |j| <= n, |i * j| <= n, and i even.

1, 3, 11, 13, 25, 27, 39, 41, 57, 59, 71, 73, 93, 95, 107, 109, 129, 131, 147, 149, 169, 171, 183, 185, 213, 215, 227, 229, 249, 251, 271, 273, 297, 299, 311, 313, 341, 343, 355, 357, 385, 387, 407, 409, 429, 431, 443, 445, 481, 483, 499, 501, 521, 523, 543, 545

Offset

0,2

Links

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

Formula

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

a(n) = A226355(n) - A270544(n).

Example

a(0) = 1 from (i,j) = (0,0).
a(1) = 3 from (i,j) = (0,0), (0,1), (0,-1).
a(2) = 11: (0,0), (0,+-1), (0,+-2), (+-2, 0), (+-2,+-1).

Mathematica

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

Prog

(PARI) a(n) = {my(nb = 0); for (i=-n, n, if ((i % 2) == 0, for(j=-n, n, if (abs(i*j) <= n, nb++); ); ); ); nb; }

Crossrefs

The corresponding sequence where i is odd is A270544.

Cf. A226355.

Sequence in context: A045429 A168164 A296933 * A213697 A287348 A019374

Adjacent sequences: A270540 A270541 A270542 * A270544 A270545 A270546

Keyword

nonn

Author

Lorenz H. Menke, Jr., Mar 18 2016

Extensions

a(44) = 429 corrected by Georg Fischer, Sep 13 2023

Status

approved