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

1,3

Links

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A304943 A248597 A082071 * A082070 A336648 A082902

Adjacent sequences: A082062 A082063 A082064 * A082066 A082067 A082068

Keyword

nonn

Author

Labos Elemer, Apr 07 2003

Extensions

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

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

Status

approved