

A002472


Number of pairs x,y such that yx=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
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OFFSET

1,4


REFERENCES

Golubev, V. A.; Nombres de Mersenne et caracteres du nombre 2. Mathesis 67 1958 257262.
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^(e1) if p = 2; (p2)*p^(e1) 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}] (* JeanFrançois 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, k1) \\ 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: A169820 A114711 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



