

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.


6



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
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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, 5n1]. [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: A097689 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



