A279507 a(n) = floor(phi(n)/tau(n)).

1, 0, 1, 0, 2, 0, 3, 1, 2, 1, 5, 0, 6, 1, 2, 1, 8, 1, 9, 1, 3, 2, 11, 1, 6, 3, 4, 2, 14, 1, 15, 2, 5, 4, 6, 1, 18, 4, 6, 2, 20, 1, 21, 3, 4, 5, 23, 1, 14, 3, 8, 4, 26, 2, 10, 3, 9, 7, 29, 1, 30, 7, 6, 4, 12, 2, 33, 5, 11, 3, 35, 2, 36, 9, 6, 6, 15, 3, 39, 3

Offset

1,5

Comments

a(n) = floor(A000010(n)/A000005(n)).

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.

Sequences b(k) of numbers n such that a(n) = k are finite for all k >=0; see A279508 (the smallest numbers n such that a(n) = k for k>=0) and A279509 (the largest numbers n such that a(n) = k for k>=0).

See A140475 (numbers n such that floor(phi(n)/tau(n)) > floor(phi(m)/tau(m)) for all m < n).

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..2000

Formula

a(n) > 1 for numbers in A279289.

Example

For n=5; a(5) = floor(phi(5)/tau(5)) = floor(4/2) = 2.

Mathematica

Table[Floor[EulerPhi[n]/DivisorSigma[0, n]], {n, 1, 25}] (* G. C. Greubel, Dec 13 2016 *)

Prog

(Magma) [Floor(EulerPhi(n)/NumberOfDivisors(n)): n in[1..100]]
(PARI) for(n=1, 25, print1(floor(eulerphi(n)/numdiv(n)), ", ")) \\ G. C. Greubel, Dec 13 2016

Crossrefs

Cf. A000005, A000010, A020488, A020490, A140475, A279289, A279508, A279509.

Sequence in context: A329646 A293813 A218585 * A054656 A080096 A322978

Adjacent sequences: A279504 A279505 A279506 * A279508 A279509 A279510

Keyword

nonn

Author

Jaroslav Krizek, Dec 13 2016

Status

approved