A082065 Greatest common prime-divisor of phi(n)=A000010(n) and sigma(2,n) = A001157(n); a(n) = 1 if no common prime-divisor exists.

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 5, 2, 2, 1, 2, 2, 3, 2, 2, 2, 1, 5, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 1, 2, 5, 2, 2, 2, 2, 2, 1, 2, 2, 5, 3, 5, 2, 2, 2, 1, 5, 2, 3, 2, 2, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2, 2, 3, 2, 1

Offset: 1

Author

Labos Elemer, Apr 07 2003

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A001157, A000010, A082061-A082066.

Programs

Maple

gcpd := proc(a,b) local g ,d ; g := 1 ; for d in numtheory[divisors](a) intersect numtheory[divisors](b) do if isprime(d) then g := max(g,d) ; end if; end do: g ; end proc:
A082065 := proc(n) gcpd( numtheory[phi](n), numtheory[sigma][2](n) ) ; end proc:
seq(A082065(n),n=1..120) ; # R. J. Mathar, Jul 09 2011

Mathematica

Table[FactorInteger[GCD[EulerPhi@ n, DivisorSigma[2, n]]][[-1, 1]], {n, 100}] (* Michael De Vlieger, Jul 22 2017 *)

PARI

gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
a(n)=gpf(gcd(eulerphi(n),sigma(n,2))) \\ Charles R Greathouse IV, Feb 21 2013

Extensions

Values corrected by R. J. Mathar, Jul 09 2011

Changed "was found" to "exists" in definition. - N. J. A. Sloane, Jan 29 2022