A279508 a(n) = smallest number k such that floor(phi(k)/tau(k)) = n.

2, 1, 5, 7, 27, 11, 13, 58, 17, 19, 55, 23, 65, 106, 29, 31, 85, 142, 37, 158, 41, 43, 115, 47, 119, 125, 53, 133, 145, 59, 61, 254, 262, 67, 274, 71, 73, 298, 1180, 79, 187, 83, 203, 346, 89, 209, 235, 382, 97, 394, 101, 103, 169, 107, 109, 253, 113, 458, 295

Offset: 0

Author

Jaroslav Krizek, Dec 13 2016

Keywords

• nonn

Comments

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

Supersequence of A045344 (primes excluding 3).

Examples

			For n = 2; a(2) = 5 because 5 is the smallest number with floor(phi(5) / tau(5)) = floor(4/2) = 2.
		

Crossrefs

Cf. A000005, A000010, A020488, A020490, A045344, A279289, A279507, A279509.

Programs

Magma

[Min([n: n in[1..100000] | Floor(EulerPhi(n)/NumberOfDivisors(n)) eq k]): k in [0..60]]

Mathematica

Table[k = 1; While[Floor[EulerPhi[k]/DivisorSigma[0, k]] != n, k++]; k, {n, 0, 58}] (* Michael De Vlieger, Dec 14 2016 *)

PARI

a(n) = my(k=1); while(floor((eulerphi(k)/numdiv(k)))!=n, k++); k \\ Felix Fröhlich, Dec 14 2016

Formula

a((p-1)/2) = p for p = prime > 3.