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A066589
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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.
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1
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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
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1,3
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), Jan 08 2002
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EXTENSIONS
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a(32)-a(33) inserted and terms a(37) and beyond from Andrew Howroyd, Jul 01 2018
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STATUS
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approved
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