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Search: id:A007427
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| A007427 |
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Moebius transform applied twice to sequence 1,0,0,0,....
(Formerly M0198)
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+0
13
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| 1, -2, -2, 1, -2, 4, -2, 0, 1, 4, -2, -2, -2, 4, 4, 0, -2, -2, -2, -2, 4, 4, -2, 0, 1, 4, 0, -2, -2, -8, -2, 0, 4, 4, 4, 1, -2, 4, 4, 0, -2, -8, -2, -2, -2, 4, -2, 0, 1, -2, 4, -2, -2, 0, 4, 0, 4, 4, -2, 4, -2, 4, -2, 0, 4, -8, -2, -2, 4, -8, -2, 0, -2, 4, -2, -2, 4, -8, -2, 0, 0
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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|a(n)| is the number of ways to write n as a product of 2 squarefree numbers (i.e. number of ways to write n = xy 1<=x<=n 1<=y<=n, x and y squarefree) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 01 2003
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
N. J. A. Sloane, Transforms
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FORMULA
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Dirichlet g.f.: 1/zeta(s)^2.
a(n)=sumd( d divides n, mu(d)*mu(n/d)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
Multiplicative with a(p^e) = (2 choose e) (-1)^e
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MATHEMATICA
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f[n_] := Plus @@ Times @@@ (MoebiusMu[{#, n/#}] & /@ Divisors@n); Array[f, 105] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1-X)^2)[n])
(PARI) a(n)=if(n<1, 0, sumdiv(n, d, moebius(d)*moebius(n/d)))
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CROSSREFS
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Dirichlet inverse of A000005.
Sequence in context: A021456 A125912 A127677 this_sequence A048106 A156260 A056671
Adjacent sequences: A007424 A007425 A007426 this_sequence A007428 A007429 A007430
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KEYWORD
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sign,easy,nice,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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