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A055734 Number of distinct primes dividing phi(n). 3
0, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 3, 3, 2, 2, 1, 3, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Murty and Murty show that the normal order of a(n) is (log log n)^2/2, that is, sum_{1 <= k <= n} a(k) ~ n/2 * (log log n)^2. - Charles R Greathouse IV, Sep 13 2013. See also Erdos-Pomerance (1985) and Erdos-Granville-et-al. (1990). - N. J. A. Sloane, Sep 02 2017

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Paul Erdős and C. Pomerance, On the normal number of prime factors of phi(n), Rocky Mountain Math. J. 15 (1985), 343-352.

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 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. [Annotated copy with A-numbers]

M. Ram Murty and V. Kumar Murty, Prime divisors of Fourier coefficients of modular forms, Duke Math. J. 51:1 (1984), pp. 57-76.

FORMULA

a(n) = A001221(A000010(n)).

MATHEMATICA

Table[PrimeNu[EulerPhi[n]], {n, 1, 50}] (* G. C. Greubel, May 08 2017 *)

PROG

(PARI) a(n)=omega(eulerphi(n)) \\ Charles R Greathouse IV, Sep 13 2013

CROSSREFS

Cf. A001221, A000010, A073918.

Sequence in context: A161274 A160978 A231776 * A295660 A193169 A193453

Adjacent sequences:  A055731 A055732 A055733 * A055735 A055736 A055737

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 11 2000

STATUS

approved

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Last modified June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)