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

Author

N. J. A. Sloane, Nov 02 2008

Keywords

• nonn

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]

Examples

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

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

Crossrefs

Cf. A000010, A097080.

Programs

PARI

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

Formula

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

Extensions

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