A235866 G-cyclic numbers: numbers n such that gcd(n,A060968(n))=1.

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 35, 37, 41, 43, 47, 51, 53, 55, 57, 59, 61, 65, 67, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 97, 101, 103, 105, 107, 109, 113, 115, 119, 123, 127, 129, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 159, 161

Offset: 1

Author

José María Grau Ribas, Jan 19 2014

Keywords

• nonn

Comments

From Robert Israel, May 01 2020: (Start)

All terms are odd and squarefree.

Contains all odd primes.

If n is a member, then so are all divisors of n.

(End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, Fermat test with Gaussian base and Gaussian pseudoprimes, arXiv:1401.4708 [math.NT], 2014.

Crossrefs

Cf. A060968, A003277.

Programs

Maple

g:= proc(p,e) if p=2 or e > 1 then 0
  elif p mod 4 = 1 then p-1 else p+1 fi
end proc:
h:= proc(n) mul(g(t[1],t[2]),t=ifactors(n)[2]) end proc:
select(n -> igcd(n,h(n))=1, [seq(i,i=1..2000,2)]); # Robert Israel, May 01 2020

Mathematica

fa=FactorInteger; phi[1]=1;phi[p_, s_] := Which[Mod[p, 4] == 1, p^(s-1)*(p-1), Mod[p, 4]==3, p^(s-1)*(p+1), s==1, 2, True, 2^(s+1)]; phi[1]=1; phi[n_] := Product[phi[fa[n][[i, 1]], fa[n][[i, 2]]], {i, Length[fa[n]]}]; Select[Range[1000], GCD[phi[#], #] == 1 &]

PARI

genit(maxx)={arr=List(); for(ptr=1, maxx, if(gcd(ptr,A060968(ptr))==1, listput(arr,ptr))); arr}
\\******** following code taken from A060968
A060968(n)={my(f=factor(n)[,1]); q=n*prod(i=if(n%2,1,2),#f,if(f[i]%4==1,1-1/f[i],1+1/f[i]))*if(n%4,1,2);return(q);} \\ Bill McEachen, Jul 16 2021