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A211271
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Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=3n.
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7
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0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 4, 2, 2, 1, 4, 2, 2, 2, 4, 1, 4, 1, 4, 2, 2, 3, 4, 1, 2, 2, 6, 1, 4, 1, 4, 3, 2, 1, 6, 2, 4, 2, 4, 1, 3, 3, 6, 2, 2, 1, 7, 1, 2, 3, 5, 3, 4, 1, 4, 2, 6, 1, 6, 1, 2, 4, 4, 3, 4, 1, 8, 2, 2, 1, 7, 3, 2, 2, 6, 1, 6, 3, 4, 2, 2, 3, 7, 1, 4, 3
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OFFSET
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1,8
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COMMENTS
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For a guide to related sequences, see A211266.
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LINKS
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EXAMPLE
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a(20) counts these pairs: (3,20), (4,15), (5,12), (6,10)
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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