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A083239 First order recursion: a(0)=1; a(n)=phi(n)-a(n-1)=A000010(n)-a(n-1). 1
1, 0, 1, 1, 1, 3, -1, 7, -3, 9, -5, 15, -11, 23, -17, 25, -17, 33, -27, 45, -37, 49, -39, 61, -53, 73, -61, 79, -67, 95, -87, 117, -101, 121, -105, 129, -117, 153, -135, 159, -143, 183, -171, 213, -193, 217, -195, 241, -225, 267, -247, 279, -255, 307, -289, 329, -305, 341, -313, 371, -355, 415, -385, 421, -389, 437, -417 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Provide interesting decomposition: phi(n)=u+w, where u and w consecutive terms of this sequence; Depends also on initial value.

It follows that a(n)+a(n-1)=A000010(n)

LINKS

Table of n, a(n) for n=0..66.

MAPLE

A083239 := proc(n)

    option remember ;

    if n = 0 then

        1 ;

    else

        numtheory[phi](n)-procname(n-1) ;

    end if;

end proc:

seq(A083239(n), n=0..100) ; # R. J. Mathar, Jun 20 2021

MATHEMATICA

f[x_] := EulerPhi[x]-f[x-1] f[0]=1; Table[f[w], {w, 1, 100}]

CROSSREFS

Cf. A000213, A083236, A083237, A083238, A000010.

Sequence in context: A292849 A115873 A329369 * A333847 A342268 A316742

Adjacent sequences:  A083236 A083237 A083238 * A083240 A083241 A083242

KEYWORD

sign

AUTHOR

Labos Elemer, Apr 23 2003

EXTENSIONS

a(0)=1 prepended. - R. J. Mathar, Jun 20 2021

STATUS

approved

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)