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A211264
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Number of integer pairs (x,y) such that 0 < x < y <= n and x*y <= n.
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10
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0, 1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 16, 17, 19, 21, 23, 24, 27, 28, 31, 33, 35, 36, 40, 41, 43, 45, 48, 49, 53, 54, 57, 59, 61, 63, 67, 68, 70, 72, 76, 77, 81, 82, 85, 88, 90, 91, 96, 97, 100, 102, 105, 106, 110, 112, 116, 118, 120, 121, 127, 128, 130, 133, 136
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OFFSET
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1,3
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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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FORMULA
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a(n) = Sum_{i=1..n} (A001222(i) mod 2)*floor(n/i)
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MAPLE
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with(numtheory): seq(add((bigomega(i) mod 2)*floor(n/i), i=1..n), n=1..60); # Ridouane Oudra, Oct 17 2019
# Alternative:
ListTools:-PartialSums(map(t-> floor(numtheory:-tau(t)/2), [$1..100])); # Robert Israel, Oct 18 2019
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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 + 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 *)
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PROG
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(Magma) [0] cat [&+[(&+[p[2]: p in Factorization(i)] mod 2) *Floor(n div i):i in [2..n] ]:n in [2..65]]; // Marius A. Burtea, Oct 17 2019
(Python)
from math import isqrt
def A211264(n): return (lambda m: sum(n//k for k in range(1, m+1))-m*(m+1)//2)(isqrt(n)) # Chai Wah Wu, Oct 08 2021
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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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