login
Numbers n such that phi(n) > tau(n).
5

%I #15 Sep 08 2022 08:46:18

%S 5,7,9,11,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,31,32,33,34,35,

%T 36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,

%U 59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77

%N Numbers n such that phi(n) > tau(n).

%C Numbers n such that A000010(n) > A000005(n).

%C There are 11 numbers n such that phi(n) <= tau(n) and 7 numbers n such that phi(n) = tau(n); see A020490 and A020488.

%C For n >= 31; phi(n) - tau(n) >= 1, see A063070.

%F a(n) = n + 11 for n >= 20.

%e 14 is a term because phi(14) = 6 > tau(14) = 4.

%t Select[Range@ 77, EulerPhi@ # > DivisorSigma[0, #] &] (* _Michael De Vlieger_, Dec 11 2016 *)

%o (Magma) [n: n in[1..1000] | EulerPhi(n) gt NumberOfDivisors(n)]

%o (PARI) is(n) = eulerphi(n) > numdiv(n) \\ _Felix Fröhlich_, Dec 09 2016

%o (PARI) a(n)=if(n<20, select(k -> eulerphi(k)>numdiv(k), [5..29])[n], n+11) \\ _Charles R Greathouse IV_, Dec 16 2016

%Y Complement of A020490.

%Y Cf. A000005, A000010, A020488, A020491, A063070, A279287, A279288.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Dec 09 2016