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A064415 a(1) = 0, a(n) = iter(n) if n is even, a(n) = iter(n)-1 if n is odd, where iter(n) = A003434(n) = smallest number of iterations of Euler totient function phi needed to reach 1. 6
0, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 4, 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 4, 6, 6, 5, 6, 5, 5, 6, 6, 5, 5, 6, 5, 6, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.

Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]

FORMULA

For all integers m >0 and n>0 a(m*n)=a(m)+a(n). The function a(n) is completely additive. The smallest integer q which satisfy the equation a(q)=n is 2^q, the greatest is 3^q. For all integers n>0, the counter image off n, a^-1(n) is finite.

a(1) = 0 and a(n) = A064415(n) for n>=2. [Joerg Arndt, Apr 08 2014]

PROG

(Haskell)

a064415 1 = 0

a064415 n = a003434 n - n `mod` 2 -- Reinhard Zumkeller, Sep 18 2011

(PARI)

A003434(n)=for(k=0, n, n>1 || return(k); n=eulerphi(n));

a(n) = if( n<=2, n-1, A003434(n) - (n%2) );

vector(200, n, a(n)) \\ Joerg Arndt, Apr 08 2014

CROSSREFS

Cf. A000010, A003434, A064416.

Cf. A054725. [From R. J. Mathar, Oct 02 2008]

Sequence in context: A241216 A125173 A054725 * A086833 A010764 A029383

Adjacent sequences:  A064412 A064413 A064414 * A064416 A064417 A064418

KEYWORD

nonn

AUTHOR

Christian WEINSBERG (cweinsbe(AT)fr.packardbell.org), Sep 30 2001

EXTENSIONS

More terms from David Wasserman, Jul 22 2002

Definition corrected by Reinhard Zumkeller, Sep 18 2011

STATUS

approved

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Last modified February 23 05:58 EST 2019. Contains 320411 sequences. (Running on oeis4.)