

A290309


Number of units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.


1



1, 1, 2, 2, 3, 2, 6, 4, 6, 3, 6, 4, 12, 6, 6, 8, 16, 6, 18, 6, 12, 6, 22, 8, 15, 12, 18, 12, 28, 6, 26, 16, 12, 16, 18, 12, 36, 18, 24, 12, 36, 12, 42, 12, 18, 22, 46, 16, 42, 15, 32, 24, 52, 18, 18, 24, 36, 28, 58, 12, 56, 26, 36, 32, 36, 12, 66, 32, 44, 18
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OFFSET

1,3


COMMENTS

If n is a prime other than 5, then a(n) = n  5 if n == 1 (mod 10), otherwise a(n) = n  1.  Robert Israel, Jul 31 2017


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


MAPLE

m:=5; T:=[]: for n from 1 to 100 do S:={}: for a from 0 to n1 do if gcd(a, n)=1 and gcd(cyclotomic(m, a), n)=1 then S:={op(S), a}: fi: od: T:=[op(T), nops(S)]: od: print(T):


MATHEMATICA

Table[Count[Range[n  1], k_ /; And[CoprimeQ[k, n], CoprimeQ[Cyclotomic[5, k], n]]], {n, 70}] (* Michael De Vlieger, Jul 30 2017 *)


PROG

(PARI) a(n) = sum(k=0, n1, (gcd(n, k)==1) && (gcd(n, polcyclo(5, k))==1)); \\ Michel Marcus, Jul 29 2017


CROSSREFS

Cf. A058026 (with Phi(1,u) or Phi(2,u)), A289460 (with Phi(3,u)).
Sequence in context: A159688 A128710 A341105 * A095757 A144368 A094438
Adjacent sequences: A290306 A290307 A290308 * A290310 A290311 A290312


KEYWORD

nonn,mult,easy


AUTHOR

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


STATUS

approved



