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A211272
Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=floor(n/2).
7
0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 2, 2, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 4, 4, 2, 2, 2, 2, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 3, 3, 2, 2, 2, 2, 2, 2, 5, 5, 1, 1, 2, 2, 2, 2, 4, 4, 1, 1, 4, 4, 1, 1, 3, 3, 3, 3, 2, 2, 1, 1, 5, 5, 2, 2
OFFSET
1,8
COMMENTS
For a guide to related sequences, see A211266.
LINKS
FORMULA
a(n) = ceiling(A000005(floor(n/2))/2). - Robert Israel, Feb 07 2020
EXAMPLE
a(24) counts these pairs: (1,12), (2,6), (3,4).
MAPLE
[seq(ceil(numtheory:-tau(floor(n/2))/2), n=1..100)]; - Robert Israel, Feb 07 2020
MATHEMATICA
a = 1; b = n; z1 = 120;
t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}] (* A038548 *)
Table[c[n, n + 1], {n, 1, z1}] (* A072670 *)
Table[c[n, 2*n], {n, 1, z1}] (* A211270 *)
Table[c[n, 3*n], {n, 1, z1}] (* A211271 *)
Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211272 *)
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Print
Table[c1[n, n], {n, 1, z1}] (* A094820 *)
Table[c1[n, n + 1], {n, 1, z1}] (* A091627 *)
Table[c1[n, 2*n], {n, 1, z1}] (* A211273 *)
Table[c1[n, 3*n], {n, 1, z1}] (* A211274 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)
PROG
(Magma) [0] cat [Ceiling(#Divisors( Floor(n/2))/2):n in [2..100]]; // Marius A. Burtea, Feb 07 2020
CROSSREFS
Sequence in context: A303827 A323116 A218344 * A298600 A292470 A293681
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 07 2012
STATUS
approved