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A002472 Number of pairs x,y such that y-x=2, (x,n)=1, (y,n)=1 and 1 <= x <= n.
(Formerly M0411 N0157)
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

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.

MATHEMATICA

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}] (* Jean-Fran├žois Alcover, Nov 22 2011 *)

PROG

(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

CROSSREFS

Sequence in context: A246186 A246179 A166285 * A060116 A114690 A238122

Adjacent sequences:  A002469 A002470 A002471 * A002473 A002474 A002475

KEYWORD

nonn,nice,easy,mult

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified August 30 22:18 EDT 2014. Contains 246232 sequences.