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A007875
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Number of ways of writing n as p*q, with p <= q, gcd(p, q) = 1.
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18
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1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 4, 1, 2, 2, 1, 2, 4, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 2, 4, 1, 2, 1, 2, 1, 4, 2, 2, 2, 2, 1, 4
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OFFSET
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1,6
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COMMENTS
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a(n), n >= 2, is the number of divisor products in the numerator as well as denominator of the unique representation of n in terms of divisor products. See the W. Lang link underA007955,where a(n)=l(n) in Table 1. -Wolfdieter Lang,Feb 08 2011
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ 3*n*((log(n) + (2*gamma - 1))/ Pi^2 - 12*(zeta'(2)/Pi^4)), where gamma is the Euler-Mascheroni constantA001620.Equivalently, Sum_{k=1..n} a(k) ~ 3*n*(log(n) + 24*log(A) - 1 - 2*log(2*Pi)) / Pi^2, where A is the Glaisher-Kinkelin constantA074962.-Vaclav Kotesovec,Jan 30 2019
Dirichlet g.f.: (zeta(s)^2/zeta(2*s) + 1)/2. -Amiram Eldar,Sep 09 2023
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MAPLE
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if n = 1 then
1;
else
end if;
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MATHEMATICA
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a[n_]:= With[{r = Reduce[1 <= p <= q <= n && n == p*q && GCD[p, q] == 1, {p, q}, Integers]}, If[Head[r] === And, 1, Length[r]]]; Table[a[n], {n, 1, 90}] (*Jean-François Alcover,Nov 02 2011 *)
a[n_]:= Sum[If[Mod[n, k] == 0, Re[Sqrt[MoebiusMu[k]]], 0], {k, 1, n}] (*Mats Granvik,Aug 10 2018 *)
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PROG
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(Haskell)
a007875 = length. filter (> 0). a225817_row
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Victor Ufnarovski
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STATUS
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approved
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