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A066589 Let u_n be the group of units mod n (invertible elements in the ring Z_n); a(n) is the number of cyclic subgroups in u_n. 1
1, 1, 2, 2, 3, 2, 4, 4, 4, 3, 4, 4, 6, 4, 6, 6, 5, 4, 6, 6, 8, 4, 4, 8, 6, 6, 6, 8, 6, 6, 8, 8, 8, 5, 12, 8, 9, 6, 12, 12, 8, 8, 8, 8, 12, 4, 4, 12, 8, 6, 10, 12, 6, 6, 12, 16, 12, 6, 4, 12, 12, 8, 20, 10, 20, 8, 8, 10, 8, 12, 8, 16, 12, 9, 12, 12, 16, 12, 8, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

PROG

(GAP) List([1..80], n->Sum( ConjugacyClasses( AutomorphismGroup( CyclicGroup(n))), x->Size(x)/Phi(Order( Representative(x)))));

(PARI) a(n)={sum(i=1, n, if(gcd(i, n)==1, 1/eulerphi(znorder(Mod(i, n)))))} \\ Andrew Howroyd, Jul 01 2018

CROSSREFS

Sequence in context: A140060 A164341 A124771 * A007897 A180783 A290731

Adjacent sequences:  A066586 A066587 A066588 * A066590 A066591 A066592

KEYWORD

nonn

AUTHOR

Sharon Sela (sharonsela(AT)hotmail.com), Jan 08 2002

EXTENSIONS

a(32)-a(33) inserted and terms a(37) and beyond from Andrew Howroyd, Jul 01 2018

STATUS

approved

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Last modified June 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)