1,3

Also number of orbits in the set of circular permutations (up to rotation) under cyclic permutation of the elements. - Michael Steyer (m.steyer(AT)osram.de), Oct 06 2001

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

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

A. Vella, Pattern avoidance in permutations: linear and cyclic orders, The Electronic J. of Combinatorics, 9(2), 2002-3, #R18.

T. D. Noe, Table of n, a(n) for n=1..100

Sum_{k|n} u(n, k)/(nk), where u(n, k) = A047918(n, k).

a(n)=(1/n^2)Sum[phi(p)^2*(n/p)!*p^(n/p)], where phi is Euler's totient function (A000010) and summation is over all divisors of n. (see the Vella reference, p. 31). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 23 2005

n=6: {(123456)}, {(135462), (246513), (351624)} and {(124635), (235146), (346251), (451362), (562413), (613524)} are 3 of the 24 orbits, consisting of 1, 3 and 6 permutations, respectively.

with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(phi(div[j])^2*(n/div[j])!*div[j]^(n/div[j]), j=1..tau(n))/n^2 end: seq(a(n), n=1..23); # (Deutsch) (Deutsch)

Cf. A002618, A047916, A064852, A064649.

Cf. A000010.

Sequence in context: A038561 A055981 A120260 this_sequence A129202 A127905 A009224

Adjacent sequences: A002616 A002617 A002618 this_sequence A002620 A002621 A002622

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), C. L. Mallows (colinm(AT)research.avayalabs.com)