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%I #5 Apr 07 2012 13:47:08
%S 0,1,3,5,7,10,12,15,18,21,24,28,30,34,38,41,44,49,51,56,60,63,67,72,
%T 75,79,83,88,91,97,99,104,109,112,117,123,125,130,135,140,143,149,152,
%U 157,163,167,170,177,180,186,190,194,199,205,209,215,219,223
%N Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=2n.
%C Guide to related sequences:
%C A056924 ... 1<=x<y<=n .... x*y=n
%C A211159 ... 1<=x<y<=n .... x*y=n+1
%C A211261 ... 1<=x<y<=n .... x*y=2n
%C A211262 ... 1<=x<y<=n .... x*y=3n
%C A211263 ... 1<=x<y<=n .... x*y=floor(n/2)
%C A211264 ... 1<=x<y<=n .... x*y<=n
%C A211265 ... 1<=x<y<=n .... x*y<=n+1
%C A211266 ... 1<=x<y<=n .... x*y<=2n
%C A211267 ... 1<=x<y<=n .... x*y<=3n
%C A181972 ... 1<=x<y<=n .... x*y<=floor(n/2)
%C A038548 ... 1<=x<=y<=n ... x*y=n
%C A072670 ... 1<=x<=y<=n ... x*y=n+1
%C A211270 ... 1<=x<=y<=n ... x*y=2n
%C A211271 ... 1<=x<=y<=n ... x*y=3n
%C A211272 ... 1<=x<=y<=n ... x*y=floor(n/2)
%C A094820 ... 1<=x<=y<=n ... x*y<=n
%C A091627 ... 1<=x<=y<=n ... x*y<=n+1
%C A211273 ... 1<=x<=y<=n ... x*y<=2n
%C A211274 ... 1<=x<=y<=n ... x*y<=3n
%C A211275 ... 1<=x<=y<=n ... x*y<=floor(n/2)
%e a(6) counts these pairs: (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4).
%t a = 1; b = n; z1 = 120;
%t t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
%t {y, x + 1, b}]]
%t c[n_, k_] := c[n, k] = Count[t[n], k]
%t Table[c[n, n], {n, 1, z1}] (* A056924 *)
%t Table[c[n, n + 1], {n, 1, z1}] (* A211159 *)
%t Table[c[n, 2*n], {n, 1, z1}] (* A211261 *)
%t Table[c[n, 3*n], {n, 1, z1}] (* A211262 *)
%t Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211263 *)
%t Print
%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
%t Table[c1[n, n], {n, 1, z1}] (* A211264 *)
%t Table[c1[n, n + 1], {n, 1, z1}] (* A211265 *)
%t Table[c1[n, 2*n], {n, 1, z1}] (* A211266 *)
%t Table[c1[n, 3*n], {n, 1, z1}] (* A211267 *)
%t Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)
%Y Cf. A211261, A211264.
%K nonn
%O 1,3
%A _Clark Kimberling_, Apr 06 2012
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