A289835 Number of units u in Z/(2n-1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.

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, 28, 50, 20, 36, 58, 58, 36, 20, 66, 44, 70, 70, 20, 60, 78, 54, 82, 28, 52, 86, 60, 60, 36, 94, 60, 98, 102, 24, 106, 106, 68, 110, 44, 60, 84, 110, 76, 50, 126, 84

Offset: 1

Author

Jordan Lenchitz, Michael Mueller, Tristan Phillips, Madison Wellen, Eric Jovinelly, Joshua Harrington, Jul 25 2017

Keywords

• nonn
• mult
• easy

Comments

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

Links

• Jordan Lenchitz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A058026, A289460.

Programs

Maple

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:

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