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Search: id:A002618
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| 1, 2, 6, 8, 20, 12, 42, 32, 54, 40, 110, 48, 156, 84, 120, 128, 272, 108, 342, 160, 252, 220, 506, 192, 500, 312, 486, 336, 812, 240, 930, 512, 660, 544, 840, 432, 1332, 684, 936, 640, 1640, 504, 1806, 880, 1080, 1012, 2162, 768, 2058, 1000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also Euler phi function of n^2.
For n >= 3 a(n) is also the size of the automorphism group of the dihedral group of order 2n. This automorphism group is isomorphic to the group of transformations x -> ax + b, where a, b and x are integers modulo n and a is coprime to n. Its order is n*phi(n). - Ola Veshta (olaveshta(AT)my-deja.com), Mar 18 2001
Order of metacyclic group of polynomial of degree n n - Artur Jasinski (grafix(AT)csl.pl), Jan 22 2008
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REFERENCES
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J. E. A. Steggall, On the numbers of patterns which can be derived from certain elements, Mess. Math., 37 (1907), 56-61.
J. L. Lagrange, Oeuvres, Vol. III Paris 1869.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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Multiplicative with a(p^e) = (p-1)*p^(2e-1). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MAPLE
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with(numtheory):a:=n->phi(n^2): seq(a(n), n=1..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
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Table[n EulerPhi[n], {n, 1, 100}] - Artur Jasinski (grafix(AT)csl.pl), Jan 22 2008
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PROGRAM
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(MuPad) numlib::phi(n^2)$ n=1..81 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008
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CROSSREFS
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First column of A047916. Cf. A002619, A047918.
See also A000010, A053650, A053191, A053192, A036689.
Cf. A058161.
Sequence in context: A072230 A028332 A124827 this_sequence A069553 A093968 A064713
Adjacent sequences: A002615 A002616 A002617 this_sequence A002619 A002620 A002621
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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njas
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EXTENSIONS
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Better description from Labos E. (labos(AT)ana.sote.hu ), Feb 18 2000.
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