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A007875
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Number of ways of writing n as pq, with p<=q, (p,q)=1.
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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| 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 under A007955, where a(n)=l(n) in Table 1. W. Lang, Feb 08 2011.
Record values are the binary powers, occurring at primorial positions except at 2: a(A001220(0))=A000079(0), a(A001220(n+1))=A000079(n) for n>0. [Reinhard Zumkeller, Aug 24 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n)= (1/2) *Sum_{ d divides n } abs(mu(d))=2^(A001221(n)-1)=A034444(n)/2, n > 1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 25 2002
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MATHEMATICA
| 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}] (* From Jean-François Alcover, Nov 02 2011 *)
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PROG
| (Haskell)
a007875 n = length [d | d <- [1..n], let (d', m) = divMod n d,
d <= d', m == 0, gcd d d' == 1]
-- Reinhard Zumkeller, Aug 24 2011
(PARI) a(n)=ceil((1<<omega(n))/2) \\ Charles R Greathouse IV, Nov 02 2011
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CROSSREFS
| Sequence in context: A001221 A064372 A096825 * A050320 A121382 A051265
Adjacent sequences: A007872 A007873 A007874 * A007876 A007877 A007878
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Victor Ufnarovski
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