

A270544


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


1



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
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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



