

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.


0



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
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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 n1 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, n1, 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 A156387
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



