

A289460


Number of units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.


6



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

1,4


COMMENTS

The number of units u in Z/nZ such that Phi(1,u) or Phi(2,u) is a unit is given by A058026.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms to 1000 from Jordan Lenchitz)


MAPLE

m:=3; T:=[]: for n from 2 to 1000 do S:={}: for a from 0 to n1 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):


MATHEMATICA

Table[Count[Map[Cyclotomic[3, #] &, Select[Range@ n, CoprimeQ[#, n] &]], u_ /; CoprimeQ[u, n]], {n, 72}] (* Michael De Vlieger, Jul 11 2017 *)


PROG

(PARI) g(n)=sum(k=0, n1, gcd(k, n)==1 && gcd(polcyclo(3, k), n)==1)
a(n)=my(f=factor(n)); prod(i=1, #f~, g(f[i, 1]^f[i, 2])) \\ Charles R Greathouse IV, Jul 06 2017


CROSSREFS

Cf. A058026.
Sequence in context: A317690 A060047 A135185 * A201774 A011029 A256696
Adjacent sequences: A289457 A289458 A289459 * A289461 A289462 A289463


KEYWORD

nonn,mult,easy


AUTHOR

Jordan Lenchitz, Michael Mueller, Tristan Phillips, Madison Wellen, Eric Jovinelly, Joshua Harrington, Jul 06 2017


STATUS

approved



