A279287 -id:A279287 - cp's OEIS frontend

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

Jaroslav Krizek, Dec 09 2016

nonn

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.

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

Complement of A020490.

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

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

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

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

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

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

A279288 a(n) = denominator of (phi(n)/tau(n)).

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 5, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 5, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 2, 1

Offset: 1

Jaroslav Krizek, Dec 09 2016

a(n) = denominator of (A000010(n)/A000005(n)).
See A279287 (numerator of (phi(n)/tau(n))) and A063070 (phi(n)-tau(n)).
a(n) = 1 and A279287(n) = 1 for numbers n in A020488; A279287(n) > a(n) for numbers n in A279289.

			For n = 6: phi(6)/tau(6) = 2/4 = 1/2; a(6) = 2.

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Cf. A000005, A000010, A020488, A020490, A020491, A063070, A279287, A279289.

[Denominator(EulerPhi(n)/NumberOfDivisors(n)): n in[1..1000]];

Table[Denominator[EulerPhi[n]/DivisorSigma[0, n]], {n, 120}] (* Michael De Vlieger, Dec 10 2016 *)

a(n) = denominator(eulerphi(n)/numdiv(n)) \\ Felix Fröhlich, Dec 09 2016

a(n) = 1 for numbers in A020491.

A290634 Positive integers which are never the quotient of phi(n)/tau(n).

Original entry on oeis.org

17, 19, 31, 38, 47, 59, 61, 62, 71, 85, 91, 101, 103, 107, 109, 118, 121, 133, 137, 149, 151, 157, 167, 181, 187, 197, 211, 217, 218, 223, 227, 229, 241, 247, 257, 259, 263, 266, 269, 271, 283, 289, 305, 311, 313, 314, 317, 327, 331, 334, 337, 347, 349, 353, 355, 361, 367

Offset: 1

Bernard Schott, Aug 08 2017

nonn

For phi(n)/tau(n) see A279287/A279288.
Numbers that do not appear in A175667.
The first nine terms of this sequence are exactly A119480(3) through A119480(11), and many other terms are common to these two sequences.

Cf. A000010, A000005, A020491, A015733, A020488, A062516, A175667, A112954, A112955, A119480, A289585, A279287/A279288.

cp's OEIS Frontend

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

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A279288 a(n) = denominator of (phi(n)/tau(n)).

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A290634 Positive integers which are never the quotient of phi(n)/tau(n).

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