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A002472
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Number of pairs x,y such that y-x=2, (x,n)=1, (y,n)=1 and 1 <= x <= n.
(Formerly M0411 N0157)
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1
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1, 1, 1, 2, 3, 1, 5, 4, 3, 3, 9, 2, 11, 5, 3, 8, 15, 3, 17, 6, 5, 9, 21, 4, 15, 11, 9, 10, 27, 3, 29, 16, 9, 15, 15, 6, 35, 17, 11, 12, 39, 5, 41, 18, 9, 21, 45, 8, 35, 15, 15, 22, 51, 9, 27, 20, 17, 27, 57, 6, 59, 29, 15, 32, 33, 9, 65, 30, 21, 15, 69, 12, 71, 35, 15, 34, 45, 11, 77, 24, 27
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OFFSET
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1,4
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REFERENCES
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Golubev, V. A.; Nombres de Mersenne et caracteres du nombre 2. Mathesis 67 1958 257-262.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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
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FORMULA
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Multiplicative with a(p^e) = p^(e-1) if p = 2; (p-2)*p^(e-1) if p > 2. - David W. Wilson, Aug 01, 2001.
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MATHEMATICA
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a[n_] := If[ Head[ r=Reduce[ GCD[x, n] == 1 && GCD[x+2, n] == 1 && 1 <= x <= n, x, Integers]] === Or, Length[r], 1]; Table[a[n], {n, 1, 81}] (* From Jean-François Alcover, Nov 22 2011 *)
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PROG
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(PARI) a(n)=my(k=valuation(n, 2), f=factor(n>>k)); prod(i=1, #f[, 1], (f[i, 1]-2)*f[i, 1]^(f[i, 2]-1))<<max(0, k-1) \\ Charles R Greathouse IV, Nov 22 2011
(Haskell)
a002472 n = length [x | x <- [1..n], gcd n x == 1, gcd n (x + 2) == 1]
-- Reinhard Zumkeller, Mar 23 2012
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CROSSREFS
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Sequence in context: A169820 A114711 A166285 * A060116 A114690 A214059
Adjacent sequences: A002469 A002470 A002471 * A002473 A002474 A002475
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KEYWORD
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nonn,nice,easy,mult,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from David W. Wilson
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STATUS
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approved
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