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
Keywords
Examples
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).
Programs
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Mathematica
a[n_]:=1+2n+2Floor[n/2]+4Sum[Floor[n/(2k)],{k,1,Floor[n/2]}] -
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;}
Formula
Extensions
a(44) = 429 corrected by Georg Fischer, Sep 13 2023