

A055684


Number of different npointed stars.


9



0, 0, 1, 0, 2, 1, 2, 1, 4, 1, 5, 2, 3, 3, 7, 2, 8, 3, 5, 4, 10, 3, 9, 5, 8, 5, 13, 3, 14, 7, 9, 7, 11, 5, 17, 8, 11, 7, 19, 5, 20, 9, 11, 10, 22, 7, 20, 9, 15, 11, 25, 8, 19, 11, 17, 13, 28, 7, 29, 14, 17, 15, 23, 9, 32, 15, 21, 11, 34, 11, 35, 17, 19, 17, 29, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

3,5


COMMENTS

Does not count rotations or reflections.
This is also the distinct ways of writing a number as the sum of two positive integers greater than one that are coprimes.  Lei Zhou, Mar 19 2014


REFERENCES

Mark A. Herkommer, "Number Theory, A Programmer's Guide," McGrawHill, New York, 1999, page 58.


LINKS

Lei Zhou, Table of n, a(n) for n = 3..10002
Alexander Bogomolny, Polygons: formality and intuition.. Includes applet to draw star polygons.
Vi Hart, Doodling in Math Class: Stars, Video (2010).
Hugo Pfoertner, Starshaped regular polygons up to n=25.
Eric Weisstein's World of Mathematics, Star Polygon


FORMULA

a(n) = A023022(n)  1.


EXAMPLE

The first star has five points and is unique. The next is the seven pointed star and it comes in two varieties.


MAPLE

with(numtheory): A055684 := n>(phi(n)2)/2; seq(A055684(n), n=3..100);


MATHEMATICA

Table[(EulerPhi[n]2)/2, {n, 3, 50}]


CROSSREFS

Cf. A023022.
Cf. A053669 smallest skip increment, A102302 skip increment of densest star polygon.
Sequence in context: A231473 A216652 A331980 * A300584 A024559 A334664
Adjacent sequences: A055681 A055682 A055683 * A055685 A055686 A055687


KEYWORD

nonn,easy


AUTHOR

Robert G. Wilson v, Jun 09 2000


STATUS

approved



