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A211267
Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=3n.
9
0, 1, 3, 6, 9, 12, 16, 20, 23, 28, 32, 37, 40, 46, 51, 56, 60, 65, 71, 77, 81, 87, 91, 99, 103, 109, 115, 121, 125, 133, 138, 145, 150, 156, 163, 169, 174, 181, 187, 196, 199, 207, 212, 220, 226, 232, 239, 247, 252, 259, 265, 274, 277, 287, 293, 301, 307
OFFSET
1,3
COMMENTS
For a guide to related sequences, see A211266.
LINKS
EXAMPLE
a(5) counts these pairs: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5).
MAPLE
N:= 100: # for a(1)..a(N)
L:= Vector(N):
for x from 1 to floor(sqrt(N)) do
for y from x+1 while y<=N and x*y<=3*N do
n0:= max(y, ceil(x*y/3));
L[n0]:= L[n0]+1;
od od:
ListTools:-PartialSums(convert(L, list)); # Robert Israel, Oct 18 2019
MATHEMATICA
a = 1; b = n; z1 = 120;
t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x + 1, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}] (* A056924 *)
Table[c[n, n + 1], {n, 1, z1}] (* A211159 *)
Table[c[n, 2*n], {n, 1, z1}] (* A211261 *)
Table[c[n, 3*n], {n, 1, z1}] (* A211262 *)
Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211263 *)
Print
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Table[c1[n, n], {n, 1, z1}] (* A211264 *)
Table[c1[n, n + 1], {n, 1, z1}] (* A211265 *)
Table[c1[n, 2*n], {n, 1, z1}] (* A211266 *)
Table[c1[n, 3*n], {n, 1, z1}] (* A211267 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
CROSSREFS
Cf. A211266.
Sequence in context: A276854 A184906 A186156 * A084515 A084525 A130248
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 06 2012
STATUS
approved