

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
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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



