login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of units u in Z/(2n-1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.
1

%I #22 Aug 03 2017 04:33:37

%S 1,2,2,6,6,10,10,4,14,18,12,22,10,18,26,30,20,12,34,20,38,42,12,46,42,

%T 28,50,20,36,58,58,36,20,66,44,70,70,20,60,78,54,82,28,52,86,60,60,36,

%U 94,60,98,102,24,106,106,68,110,44,60,84,110,76,50,126,84

%N Number of units u in Z/(2n-1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.

%C If k is even, the number of units u in Z/kZ such that Phi(4,u) is a unit is zero.

%H Jordan Lenchitz, <a href="/A289835/b289835.txt">Table of n, a(n) for n = 1..1000</a>

%p m:=4 do for t from 1 to 1000 do n:=2*t-1: 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: print(t,nops(S)): od: od:

%o (PARI) a(n) = sum(k=0, 2*n-2, (gcd(2*n-1, k)==1) && (gcd(2*n-1, polcyclo(4, k))==1)); \\ _Michel Marcus_, Jul 29 2017

%Y Cf. A058026, A289460.

%K nonn,mult,easy

%O 1,2

%A _Jordan Lenchitz_, _Michael Mueller_, _Tristan Phillips_, _Madison Wellen_, _Eric Jovinelly_, _Joshua Harrington_, Jul 25 2017