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

2,2

Links

Table of n, a(n) for n=2..79.

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 *)

Prog

(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

Crossrefs

Cf. A058026, A289460.

Sequence in context: A202992 A158830 A275744 * A145430 A143160 A369730

Adjacent sequences: A290318 A290319 A290320 * A290322 A290323 A290324

Keyword

nonn

Author

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

Status

approved