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A055684 Number of different n-pointed stars. 7
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," McGraw-Hill, 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, Star-shaped 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: A287477 A231473 A216652 * A300584 A024559 A061797

Adjacent sequences:  A055681 A055682 A055683 * A055685 A055686 A055687

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v, Jun 09 2000

STATUS

approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)