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A055205
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Number of nonsquare divisors of n^2.
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10
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0, 1, 1, 2, 1, 5, 1, 3, 2, 5, 1, 9, 1, 5, 5, 4, 1, 9, 1, 9, 5, 5, 1, 13, 2, 5, 3, 9, 1, 19, 1, 5, 5, 5, 5, 16, 1, 5, 5, 13, 1, 19, 1, 9, 9, 5, 1, 17, 2, 9, 5, 9, 1, 13, 5, 13, 5, 5, 1, 33, 1, 5, 9, 6, 5, 19, 1, 9, 5, 19, 1, 23, 1, 5, 9, 9, 5, 19, 1, 17, 4, 5, 1, 33, 5, 5, 5, 13, 1, 33, 5, 9, 5, 5, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| a(n) = A048691(n) - A000005(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 08 2009]
a(n) = A056595(A000290(n)).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = A000005(n^2)-A000005(n) because the number of square divisors of n^2 equals the number of divisors of n.
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EXAMPLE
| n = 8, d(64) = 7 and from the 7 divisors {1,4,16,64} are square and the remaining 3 = a(8). n = 12, d(144) = 15, from which 6 divisors are squares {1,4,9,16,36,144} so a(12) = d(144)-d(12) = 9
a(60) = (number of terms of finite A171425) = 33. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 08 2009]
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MATHEMATICA
| Table[Count[Divisors[n^2], d_ /; ! IntegerQ[Sqrt[d]]], {n, 1, 95}] (* Jean-François Alcover Mar 22 2011 *)
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PROG
| (Haskell)
a055205 n = length [d | d <- [1..n^2], n^2 `mod` d == 0, a010052 d == 0]
-- Reinhard Zumkeller, Aug 15 2011
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CROSSREFS
| A000005.
Sequence in context: A047818 A055972 A079168 * A161686 A069626 A205443
Adjacent sequences: A055202 A055203 A055204 * A055206 A055207 A055208
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KEYWORD
| nice,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jun 19 2000
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