A279509 a(n) = largest number k such that floor(phi(k)/tau(k)) = n.

12, 60, 180, 240, 420, 480, 840, 462, 1260, 1680, 1440, 690, 2520, 2100, 2160, 2310, 3360, 2400, 3780, 5040, 4620, 3600, 3300, 1410, 5460, 4080, 6300, 7560, 5880, 4140, 9240, 2646, 10080, 6600, 6480, 7200, 10920, 8820, 9360, 2370, 13860, 8640, 8160, 15120

Offset: 0

Author

Jaroslav Krizek, Dec 19 2016

Keywords

• nonn

Comments

a(n) = largest number k such that floor(A000010(k)/A000005(k)) = A279507(k) = n.

Sequences b_n of numbers k such that floor(phi(k)/tau(k)) = n for n = 0..2:

b_0: 2, 4, 6, 12;

b_1: 1, 3, 8, 10, 14, 16, 18, 20, 24, 30, 36, 42, 48, 60;

b_2: 5, 9, 15, 22, 28, 32, 40, 54, 66, 72, 84, 90, 96, 120, 180.

Sequences b_n are finite for all n >= 0. See A279508 (smallest number k such that floor(phi(k)/tau(k)) = n).

Examples

			For n = 1; a(1) = 60 because 60 is the largest number with floor(phi(60)/tau(60)) = floor(16/12) = 1.
		

Crossrefs

Cf. A000005, A000010, A020488, A020490, A279289, A279507, A279508.

Programs

Magma

[Max([n: n in[1..100000] | Floor(EulerPhi(n) / NumberOfDivisors(n)) eq k]): k in [0..50]]