A279289 Numbers k such that phi(k) > tau(k).

5, 7, 9, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

Jaroslav Krizek, Dec 09 2016

Keywords

• nonn

Comments

Numbers k such that A000010(k) > A000005(k).

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

For k >= 31; phi(k) - tau(k) >= 1, see A063070.

Examples

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

Crossrefs

Complement of A020490.

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

Programs

Magma

[n: n in[1..1000] | EulerPhi(n) gt NumberOfDivisors(n)];

Mathematica

Select[Range@ 77, EulerPhi@ # > DivisorSigma[0, #] &] (* Michael De Vlieger, Dec 11 2016 *)

PARI

is(n) = eulerphi(n) > numdiv(n) \\ Felix Fröhlich, Dec 09 2016

PARI

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

Formula

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