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A055034
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a(1) = 1, a(n) = phi(2*n)/2 for n>1.
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10
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1, 1, 1, 2, 2, 2, 3, 4, 3, 4, 5, 4, 6, 6, 4, 8, 8, 6, 9, 8, 6, 10, 11, 8, 10, 12, 9, 12, 14, 8, 15, 16, 10, 16, 12, 12, 18, 18, 12, 16, 20, 12, 21, 20, 12, 22, 23, 16, 21, 20, 16, 24, 26, 18, 20, 24, 18, 28, 29, 16, 30, 30, 18, 32, 24, 20, 33, 32, 22, 24, 35, 24, 36, 36, 20, 36, 30
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| For n>1, gives number of times n appears in A094192. - Lekraj Beedassy, Jun 04 2004
Number of integers less than n and having the opposite parity to n that are relatively prime to n. - Anne M. Donovan (anned3005(AT)aol.com), Jul 18 2005
Degree of minimal polynomial of cos(pi/n) over the rationals. For the minimal polynomials of 2*cos(pi/n), n>=1, see A187360. - Wolfdieter Lang, Jul 19 2011.
a(n) is, for n>=2, the number of (positive) odd numbers 2*k+1 < n satisfying gcd(2*k+1,n)=1. See the formula for the zeros of the minmial polynomials A187360. E.g., n=10: 1,3,7,9, hence a(10)=4. - Wolfdieter Lang, Aug 17 2011.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..2000
Eric Weisstein's World of Mathematics, Trigonometry Angles
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MATHEMATICA
| Join[{1}, EulerPhi[2*Range[2, 100]]/2] (* From Harvey P. Dale, Aug 12 2011 *)
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CROSSREFS
| Cf. A000010.
Sequence in context: A155940 A186963 A060473 * A112184 A112213 A085755
Adjacent sequences: A055031 A055032 A055033 * A055035 A055036 A055037
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KEYWORD
| easy,nonn
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AUTHOR
| Shawn Cokus (Cokus(AT)math.washington.edu)
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EXTENSIONS
| Better description from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2002
Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 20 2005
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