A290321 Sum modulo n of all units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.

1, 2, 0, 0, 5, 1, 0, 6, 0, 0, 4, 1, 8, 5, 0, 0, 15, 1, 0, 8, 0, 0, 8, 0, 14, 18, 16, 0, 20, 1, 0, 11, 0, 25, 12, 1, 20, 14, 0, 0, 8, 1, 0, 15, 0, 0, 16, 7, 0, 17, 28, 0, 45, 0, 32, 20, 0, 0, 40, 1, 32, 24, 0, 30, 44, 1, 0, 23, 60, 0, 24, 1, 38, 25, 40, 66, 14, 1

Offset: 2

Author

Michael Mueller, Jordan Lenchitz, Tristan Phillips, Madison Wellen, Eric Jovinelly, Joshua Harrington, Jul 27 2017

Keywords

• nonn

Crossrefs

Cf. A058026, A289460.

Programs

Maple

with(numtheory): m:=3: for n from 2 to 100 do S:={}: for a from 1 to n-1 do if gcd(a,n)=1 and gcd(cyclotomic(m,a),n)=1 then S:={op(S),a}: fi: od: print(sum(op(i,S),i=1..nops(S)) mod n): od:

Mathematica

Table[Mod[Total@ Select[Range[n - 1], CoprimeQ[#, n] && CoprimeQ[Cyclotomic[3, #], n] &], n], {n, 79}] (* Michael De Vlieger, Jul 29 2017 *)

PARI

a(n) = sum(k=0, n-1, k*((gcd(n, k)==1) && (gcd(n, polcyclo(3, k))==1))) % n; \\ Michel Marcus, Jul 29 2017