A290322 Sum modulo n of all units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.

1, 0, 0, 4, 0, 0, 0, 0, 9, 1, 0, 0, 0, 3, 0, 0, 0, 0, 8, 0, 12, 0, 0, 20, 0, 0, 0, 0, 18, 1, 0, 24, 0, 14, 0, 0, 0, 0, 16, 1, 0, 0, 24, 9, 0, 0, 0, 0, 45, 0, 0, 0, 0, 14, 0, 0, 0, 0, 36, 1, 32, 0, 0, 13, 24, 0, 0, 0, 14, 1, 0, 0, 0, 15, 0, 28, 0, 0, 32, 0, 42, 0

Offset

2,4

Comments

Conjecture: If n is divisible by 5 then a(n) > 0. - Robert Israel, Jan 23 2024

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Maple

with(numtheory): m:=5: 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[5, #], n] &], n], {n, 83}] (* Michael De Vlieger, Jul 29 2017 *)

Prog

(PARI) a(n) = sum(k=0, n-1, k*((gcd(n, k)==1) && (gcd(n, polcyclo(5, k))==1))) % n; \\ Michel Marcus, Jul 29 2017

Crossrefs

Cf. A058026, A289460.

Sequence in context: A331437 A351572 A108708 * A274948 A005925 A333037

Adjacent sequences: A290319 A290320 A290321 * A290323 A290324 A290325

Keyword

nonn,look

Author

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

Status

approved