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A082071 Smallest common prime-divisor of phi(n) = A000010(n) and sigma_2(n) = A001157(n); a(n)=1 if no common prime-divisor exists.

%I A082071 #22 Jan 29 2022 13:04:59
%S A082071 1,1,2,1,2,2,2,1,1,2,2,2,2,2,2,1,2,1,2,2,2,2,2,2,1,2,2,2,2,2,2,1,2,2,
%T A082071 2,3,2,2,2,2,2,2,2,2,2,2,2,2,3,5,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,
%U A082071 2,2,2,1,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,1,2,2,2,2,2
%N A082071 Smallest common prime-divisor of phi(n) = A000010(n) and sigma_2(n) = A001157(n); a(n)=1 if no common prime-divisor exists.
%H A082071 Antti Karttunen, <a href="/A082071/b082071.txt">Table of n, a(n) for n = 1..16384</a>
%F A082071 a(n) = A020639(gcd(A000010(n), A001157(n))). - _Antti Karttunen_, Nov 03 2017
%t A082071 Array[If[CoprimeQ[#1, #2], 1, Min@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {EulerPhi@ #,
%t A082071 DivisorSigma[2, #]} &, 105] (* _Michael De Vlieger_, Nov 03 2017 *)
%o A082071 (PARI)
%o A082071 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A082071 A082071(n) = A020639(gcd(eulerphi(n),sigma(n,2))); \\ _Antti Karttunen_, Nov 03 2017
%Y A082071 Cf. A000010, A001157, A020639.
%Y A082071 Cf. also A082065, A082067, A082068, A082069, A082070, A082072.
%K A082071 nonn
%O A082071 1,3
%A A082071 _Labos Elemer_, Apr 07 2003
%E A082071 Values corrected by _R. J. Mathar_, Jul 09 2011
%E A082071 More terms from _Antti Karttunen_, Nov 03 2017
%E A082071 Changed "was found" to "exists" in definition. - _N. J. A. Sloane_, Jan 29 2022