login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

%I M0411 N0157

%S 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,

%T 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,

%U 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

%N Number of pairs x,y such that y-x=2, (x,n)=1, (y,n)=1 and 1 <= x <= n.

%D Golubev, V. A.; Nombres de Mersenne et caracteres du nombre 2. Mathesis 67 1958 257-262.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002472/b002472.txt">Table of n, a(n) for n = 1..1000</a>

%F 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.

%t 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 *)

%o (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

%o (Haskell)

%o a002472 n = length [x | x <- [1..n], gcd n x == 1, gcd n (x + 2) == 1]

%o -- _Reinhard Zumkeller_, Mar 23 2012

%K nonn,nice,easy,mult

%O 1,4

%A _N. J. A. Sloane_.

%E More terms from _David W. Wilson_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 28 22:38 EST 2014. Contains 250438 sequences.