cp's OEIS Frontend

A289460 Number of units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.

%I A289460 #33 Jul 12 2017 07:28:53
%S A289460 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,
%T A289460 28,16,10,16,16,6,34,16,10,16,40,4,40,20,12,22,46,8,28,20,16,20,52,9,
%U A289460 40,16,16,28,58,8,58,28,12,32,40,10,64,32,22,16,70,12
%N A289460 Number of units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.
%C A289460 The number of units u in Z/nZ such that Phi(1,u) or Phi(2,u) is a unit is given by A058026.
%H A289460 Charles R Greathouse IV, <a href="/A289460/b289460.txt">Table of n, a(n) for n = 1..10000</a> (terms to 1000 from Jordan Lenchitz)
%p A289460 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):
%t A289460 Table[Count[Map[Cyclotomic[3, #] &, Select[Range@ n, CoprimeQ[#, n] &]], u_ /; CoprimeQ[u, n]], {n, 72}] (* _Michael De Vlieger_, Jul 11 2017 *)
%o A289460 (PARI) g(n)=sum(k=0,n-1, gcd(k,n)==1 && gcd(polcyclo(3,k),n)==1)
%o A289460 a(n)=my(f=factor(n)); prod(i=1,#f~, g(f[i,1]^f[i,2])) \\ _Charles R Greathouse IV_, Jul 06 2017
%Y A289460 Cf. A058026.
%K A289460 nonn,mult,easy
%O A289460 1,4
%A A289460 _Jordan Lenchitz_, _Michael Mueller_, _Tristan Phillips_, _Madison Wellen_, _Eric Jovinelly_, _Joshua Harrington_, Jul 06 2017