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Difference between number of prime factors of n and of phi(n).
1

%I #14 May 19 2017 20:34:32

%S 0,1,0,0,0,1,-1,0,-1,1,-1,1,-1,0,1,0,0,0,-1,1,0,0,-1,1,-1,0,-1,0,-1,2,

%T -2,0,0,1,0,0,-1,0,0,1,-1,1,-2,0,0,0,-1,1,-2,0,1,0,-1,0,0,0,0,0,-1,2,

%U -2,-1,0,0,0,1,-2,1,0,1,-2,0,-1,0,0,0,-1,1,-2,1,-1,0,-1,1,1,-1,0,0,-1

%N Difference between number of prime factors of n and of phi(n).

%C Prime factors counted without multiplicity. - _Harvey P. Dale_, Mar 03 2016

%C The first term with an absolute value greater than 2 is a(211); the first term with an absolute value greater than 3 is a(2311); the first term with an absolute value greater than 4 is a(43891). - _Harvey P. Dale_, Mar 03 2016

%H G. C. Greubel, <a href="/A055736/b055736.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A001221(n) - A001221(A000010(n)).

%e For n=105, phi(n)=48, with 3 or 2 prime factors respectively, so a(105) = 3 - 2 = 1.

%t Table[PrimeNu[n]-PrimeNu[EulerPhi[n]],{n,90}] (* _Harvey P. Dale_, Mar 03 2016 *)

%o (PARI) for(n=1,50, print1(omega(n) - omega(eulerphi(n)), ", ")) \\ _G. C. Greubel_, May 19 2017

%Y Cf. A000010, A001221.

%K sign

%O 1,30

%A _Labos Elemer_, Jul 11 2000