A097604 - OEIS

%I #11 Sep 08 2022 08:45:14

%S 0,0,1,1,7,0,15,8,16,7,35,7,48,17,28,29,76,18,91,30,56,44,126,31,116,

%T 60,105,61,184,31,205,96,129,97,165,65,272,118,172,103,321,67,346,143,

%U 182,165,398,108,366,150,272,192,482,133,364,197,327,243,571,115,601,272,341

%N a(n) = floor( phi(n)*sqrt(2*n) ) - n.

%C This is known to be always >= 0, i.e. that n/phi(n) <= sqrt(2n) holds for all n. This is a consequence of the stronger inequality in A079530.

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

%H G. C. Greubel, <a href="/A097604/b097604.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Floor[Sqrt[2*n]*EulerPhi[n]] - n, {n, 1, 100}] (* _G. C. Greubel_, Jan 14 2019 *)

%o (PARI) vector(100, n, (sqrt(2*n)*eulerphi(n))\1 -n) \\ _G. C. Greubel_, Jan 14 2019

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

%o (Sage) [floor(sqrt(2*n)*euler_phi(n)) - n for n in (1..100)] # _G. C. Greubel_, Jan 14 2019

%Y Cf. A079530, A097850.

%K nonn

%O 1,5

%A _N. J. A. Sloane_, based on emails from _Alonso del Arte_ and _Jud McCranie_, Aug 30 2004