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%I #17 Aug 01 2017 02:22:40
%S 1,1,2,2,3,2,6,4,6,3,6,4,12,6,6,8,16,6,18,6,12,6,22,8,15,12,18,12,28,
%T 6,26,16,12,16,18,12,36,18,24,12,36,12,42,12,18,22,46,16,42,15,32,24,
%U 52,18,18,24,36,28,58,12,56,26,36,32,36,12,66,32,44,18
%N Number of units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.
%C If n is a prime other than 5, then a(n) = n - 5 if n == 1 (mod 10), otherwise a(n) = n - 1. - _Robert Israel_, Jul 31 2017
%H Robert Israel, <a href="/A290309/b290309.txt">Table of n, a(n) for n = 1..10000</a>
%p m:=5; T:=[]: for n from 1 to 100 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(T):
%t Table[Count[Range[n - 1], k_ /; And[CoprimeQ[k, n], CoprimeQ[Cyclotomic[5, k], n]]], {n, 70}] (* _Michael De Vlieger_, Jul 30 2017 *)
%o (PARI) a(n) = sum(k=0, n-1, (gcd(n, k)==1) && (gcd(n, polcyclo(5, k))==1)); \\ _Michel Marcus_, Jul 29 2017
%Y Cf. A058026 (with Phi(1,u) or Phi(2,u)), A289460 (with Phi(3,u)).
%K nonn,mult,easy
%O 1,3
%A _Tristan Phillips_, _Jordan Lenchitz_, _Michael Mueller_, _Madison Wellen_, _Eric Jovinelly_, _Joshua Harrington_, Jul 27 2017
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