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A211261
Number of integer pairs (x,y) such that 0<x<y<=n and x*y=2n.
10
0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 3, 3, 2, 1, 4, 2, 2, 3, 3, 1, 5, 1, 2, 3, 2, 3, 5, 1, 2, 3, 4, 1, 5, 1, 3, 5, 2, 1, 5, 2, 3, 3, 3, 1, 5, 3, 4, 3, 2, 1, 7, 1, 2, 5, 3, 3, 5, 1, 3, 3, 5, 1, 6, 1, 2, 5, 3, 3, 5, 1, 5, 4, 2, 1, 7, 3, 2, 3, 4, 1, 8, 3, 3, 3, 2, 3, 6, 1, 3, 5
OFFSET
1,6
COMMENTS
For a guide to related sequences, see A211266.
LINKS
FORMULA
a(n) = floor(A000005(2*n)/2)-1. - Antti Karttunen, Sep 30 2018, after David A. Corneth's PARI-program
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 *)
PROG
(PARI) A211261(n) = sumdiv(2*n, y, (((2*n/y)<y)&&(y<=n))); \\ Antti Karttunen, Sep 30 2018
(PARI) a(n) = numdiv(n<<1)>>1-1 \\ David A. Corneth, Sep 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 06 2012
STATUS
approved