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A289460
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Number of units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.
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6
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1, 1, 1, 2, 4, 1, 4, 4, 3, 4, 10, 2, 10, 4, 4, 8, 16, 3, 16, 8, 4, 10, 22, 4, 20, 10, 9, 8, 28, 4, 28, 16, 10, 16, 16, 6, 34, 16, 10, 16, 40, 4, 40, 20, 12, 22, 46, 8, 28, 20, 16, 20, 52, 9, 40, 16, 16, 28, 58, 8, 58, 28, 12, 32, 40, 10, 64, 32, 22, 16, 70, 12
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OFFSET
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1,4
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COMMENTS
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The number of units u in Z/nZ such that Phi(1,u) or Phi(2,u) is a unit is given by A058026.
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LINKS
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MAPLE
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m:=3; T:=[]: for n from 2 to 1000 do S:={}: for a from 0 to n-1 do if gcd(a, n)=1 and gcd(cyclotomic(m, a), n)=1 then S:={op(S), a}: fi: od: T:=[op(T), nops(S)]: od: print(m, T):
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MATHEMATICA
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Table[Count[Map[Cyclotomic[3, #] &, Select[Range@ n, CoprimeQ[#, n] &]], u_ /; CoprimeQ[u, n]], {n, 72}] (* Michael De Vlieger, Jul 11 2017 *)
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PROG
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(PARI) g(n)=sum(k=0, n-1, gcd(k, n)==1 && gcd(polcyclo(3, k), n)==1)
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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