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A111076
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Smallest positive number of maximal order mod n.
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10
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1, 1, 2, 3, 2, 5, 3, 3, 2, 3, 2, 5, 2, 3, 2, 3, 3, 5, 2, 3, 2, 7, 5, 5, 2, 7, 2, 3, 2, 7, 3, 3, 2, 3, 2, 5, 2, 3, 2, 3, 6, 5, 3, 3, 2, 5, 5, 5, 3, 3, 5, 7, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 7, 5, 5, 5, 2, 3, 2, 7, 3, 3, 2, 7, 2, 5, 3, 3, 2, 3, 3, 7, 2, 3, 11, 5, 2, 5, 5, 3, 2, 3
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OFFSET
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1,3
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A229708(n) if and only if a(n) is prime. - Jonathan Sondow, May 17 2017
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EXAMPLE
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a(6)=5 because order of 1 is 1 and 2 through 4 are not relatively prime to 6, but 5 has order 2, which is the maximum possible.
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MATHEMATICA
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Table[Min[
Select[Range[n],
CoprimeQ[#, n] &&
MultiplicativeOrder[#, n] == CarmichaelLambda[n] &]], {n, 1, 100}]
(* Geoffrey Critzer, Jan 04 2015 *)
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PROG
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(PARI) a(n)=if(n==1, return(1)); if(n<5, return(n-1)); my(o=lcm(znstar(n)[2]), k=1); while(gcd(k++, n)>1 || znorder(Mod(k, n))<o, ); k \\ Charles R Greathouse IV, Jul 31 2013
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CROSSREFS
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Cf. A002322 (orders); same as A046145 for n with primitive roots; see also A001918 (for primes), A229708.
Sequence in context: A029600 A169616 A344448 * A162398 A131470 A352708
Adjacent sequences: A111073 A111074 A111075 * A111077 A111078 A111079
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KEYWORD
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easy,nonn
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AUTHOR
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Franklin T. Adams-Watters, Oct 10 2005
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STATUS
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approved
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