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a(n) = phi(n) - ceiling(n^(2/3)).
5

%I #12 Sep 08 2022 08:45:08

%S 0,-1,-1,-1,1,-2,2,0,1,-1,5,-2,6,0,1,1,9,-1,10,0,4,2,13,-1,11,3,9,2,

%T 18,-2,20,5,9,5,13,1,24,6,12,4,28,-1,29,7,11,9,32,2,28,6,18,10,37,3,

%U 25,9,21,13,42,0,44,14,20,16,31,3,49,15,27,7,52,6,54,18,22,18,41,5,59,13,35,21,62,4,44,22

%N a(n) = phi(n) - ceiling(n^(2/3)).

%C a(n) >= 0 for n > 30.

%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 9.

%H G. C. Greubel, <a href="/A079531/b079531.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[EulerPhi[n]-Ceiling[Surd[n,3]^2],{n,90}] (* _Harvey P. Dale_, Oct 27 2016 *)

%o (PARI) a(n)=eulerphi(n)-sqrtnint(n^2-1,3)-1 \\ _Charles R Greathouse IV_, Feb 07 2013

%o (Magma) [EulerPhi(n) - Ceiling(n^(2/3)): n in [1..100]]; // _G. C. Greubel_, Jan 14 2019

%o (Sage) [euler_phi(n) - ceil(n^(2/3)) for n in (1..100)] # _G. C. Greubel_, Jan 14 2019

%Y Cf. A000010, A079530, A079532, A079534.

%K sign,easy

%O 1,6

%A _N. J. A. Sloane_, Jan 23 2003