# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a055734 Showing 1-1 of 1 %I A055734 #30 Apr 26 2019 15:56:59 %S A055734 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, %T A055734 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, %U A055734 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 %N A055734 Number of distinct primes dividing phi(n). %C A055734 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 %H A055734 Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 %H A055734 Paul Erdős and C. Pomerance, On the normal number of prime factors of phi(n), Rocky Mountain Math. J. 15 (1985), 343-352. %H A055734 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. %H A055734 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] %H A055734 M. Ram Murty and V. Kumar Murty, Prime divisors of Fourier coefficients of modular forms, Duke Math. J. 51:1 (1984), pp. 57-76. %F A055734 a(n) = A001221(A000010(n)). %t A055734 Table[PrimeNu[EulerPhi[n]], {n, 1, 50}] (* _G. C. Greubel_, May 08 2017 *) %o A055734 (PARI) a(n)=omega(eulerphi(n)) \\ _Charles R Greathouse IV_, Sep 13 2013 %Y A055734 Cf. A001221, A000010, A073918. %K A055734 nonn %O A055734 1,7 %A A055734 _Labos Elemer_, Jul 11 2000 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE