A002246 a(1) = 3; for n > 1, a(n) = 4*phi(n); given a rational number r = p/q, where q>0, (p,q)=1, define its height to be max{|p|,q}; then a(n) = number of rational numbers of height n.

3, 4, 8, 8, 16, 8, 24, 16, 24, 16, 40, 16, 48, 24, 32, 32, 64, 24, 72, 32, 48, 40, 88, 32, 80, 48, 72, 48, 112, 32, 120, 64, 80, 64, 96, 48, 144, 72, 96, 64, 160, 48, 168, 80, 96, 88, 184, 64, 168, 80, 128, 96, 208, 72, 160, 96, 144, 112, 232, 64, 240, 120, 144, 128, 192, 80, 264

Offset

1,1

Comments

The old entry with this sequence number was a duplicate of A008831.

a(n) is also the number of integers prime to n in the interval [n+1, 5n-1]. [From Washington Bomfim, Oct 10 2009]

References

M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 7.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(1) = 3; thereafter a(n) = 4*phi(n) = 4*A000010(n).

Example

The three rational numbers of height 1 are 0, 1 and -1.

Prog

(PARI) A002246(n) = if(1==n, 3, 4*eulerphi(n)); \\ Antti Karttunen, Dec 05 2017

Crossrefs

Cf. A000010, A097080.

Sequence in context: A349609 A258326 A308769 * A310016 A030014 A047968

Adjacent sequences: A002243 A002244 A002245 * A002247 A002248 A002249

Keyword

nonn

Author

N. J. A. Sloane, Nov 02 2008

Extensions

A simpler alternative description added to the name field by Antti Karttunen, Dec 05 2017

Status

approved