1,2

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

It appears that this sequence gives the number of permutations of 1,2,3...,n that are arithmetic progressions modulo n. [From John W. Layman (layman(AT)math.vt.edu), Aug 27 2008]

The conjecture by Layman is correct. Obviously any such permutation must have an increment that is prime to n, and almost as obvious that any such increment will work, with any starting value; hence phi(n) * n total. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 09 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

T. D. Noe, Table of n, a(n) for n=1..1000

Multiplicative with a(p^e) = (p-1)*p^(2e-1). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

with(numtheory):a:=n->phi(n^2): seq(a(n), n=1..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007

with(numtheory):seq(sum(phi(n), k=1..n), n=1..36); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]

Table[n EulerPhi[n], {n, 1, 100}] - Artur Jasinski (grafix(AT)csl.pl), Jan 22 2008

(MuPad) numlib::phi(n^2)$ n=1..81 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008

(Other) sage: [euler_phi(n^2)for n in xrange(1, 51)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]

First column of A047916. Cf. A002619, A047918.

See also A000010, A053650, A053191, A053192, A036689.

Cf. A058161.

Sequence in context: A028332 A124827 A140965 this_sequence A069553 A143481 A093968

Adjacent sequences: A002615 A002616 A002617 this_sequence A002619 A002620 A002621

nonn,easy,nice,mult

N. J. A. Sloane (njas(AT)research.att.com).

Better description from Labos E. (labos(AT)ana.sote.hu ), Feb 18 2000.