cp's OEIS Frontend

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.

%I A082065 #19 Jan 29 2022 13:11:33
%S A082065 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,
%T A082065 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,
%U A082065 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
%N 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.
%H A082065 Michael De Vlieger, <a href="/A082065/b082065.txt">Table of n, a(n) for n = 1..10000</a>
%p A082065 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:
%p A082065 A082065 := proc(n) gcpd( numtheory[phi](n), numtheory[sigma][2](n) ) ; end proc:
%p A082065 seq(A082065(n),n=1..120) ; # _R. J. Mathar_, Jul 09 2011
%t A082065 Table[FactorInteger[GCD[EulerPhi@ n, DivisorSigma[2, n]]][[-1, 1]], {n, 100}] (* _Michael De Vlieger_, Jul 22 2017 *)
%o A082065 (PARI) gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
%o A082065 a(n)=gpf(gcd(eulerphi(n),sigma(n,2))) \\ _Charles R Greathouse IV_, Feb 21 2013
%Y A082065 Cf. A006530, A001157, A000010, A082061-A082066.
%K A082065 nonn
%O A082065 1,3
%A A082065 _Labos Elemer_, Apr 07 2003
%E A082065 Values corrected by _R. J. Mathar_, Jul 09 2011
%E A082065 Changed "was found" to "exists" in definition. - _N. J. A. Sloane_, Jan 29 2022