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A059885
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a(n)=|{m : multiplicative order of 3 mod m=n}|.
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13
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2, 2, 2, 6, 4, 10, 2, 14, 4, 16, 6, 58, 2, 10, 16, 88, 6, 108, 6, 150, 10, 54, 6, 290, 18, 10, 56, 138, 14, 716, 14, 144, 22, 118, 40, 1088, 6, 54, 90, 670, 14, 730, 6, 570, 356, 22, 30, 13864, 124, 342
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The multiplicative order of a mod m, GCD(a,m)=1, is the smallest natural number d for which a^d = 1 (mod m). a(n)=number of orders of degree-n monic irreducible polynomials over GF(3).
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FORMULA
| a(n)=Sum_{ d divides n } mu(n/d)*tau(3^d-1), (mu(n) = Moebius function A008683, tau(n) = number of divisors of n A000005).
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EXAMPLE
| a(2)=|{4,8}|=2, a(4)=|{5,10,16,20,40,80}|=6, a(6)=|{7,14,28,52,56,91,104,182,364,728}|=10,...
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MAPLE
| with(numtheory); A059885 := proc(n) local d, s; s := 0; for d in divisors(n) do s := s+mobius(n/d)*tau(3^d-1); od; RETURN(s); end;
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CROSSREFS
| Cf. A000005, A008683, A027376, A058944, A059499, A059886-A059892.
Sequence in context: A099259 A131904 A038074 * A145890 A097091 A094204
Adjacent sequences: A059882 A059883 A059884 * A059886 A059887 A059888
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 06 2001
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