cp's OEIS Frontend

A082066 Greatest common prime-divisor of sigma_1(n)=A000203(n) and sigma_2(n)=A001157(n); a(n)=1 if no common prime-divisor exists.

%I A082066 #20 Jan 29 2022 13:10:59
%S A082066 1,1,2,7,2,2,2,5,13,2,2,7,2,2,2,31,2,13,2,7,2,2,2,5,31,2,5,7,2,2,2,7,
%T A082066 2,2,2,13,2,5,2,5,2,2,2,7,13,2,2,31,19,31,2,7,2,5,2,5,5,5,2,7,2,2,13,
%U A082066 127,2,2,2,7,2,2,2,13,2,2,31,7,2,2,2,31,11,2,2,7,2,2,5,5,2,13,2,7,2,2,2,7,2
%N A082066 Greatest common prime-divisor of sigma_1(n)=A000203(n) and sigma_2(n)=A001157(n); a(n)=1 if no common prime-divisor exists.
%H A082066 Antti Karttunen, <a href="/A082066/b082066.txt">Table of n, a(n) for n = 1..10000</a>
%F A082066 a(n) = A006530(A179931(n)). - _Reinhard Zumkeller_, Jul 10 2011
%t A082066 ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] f1[x_] := DivisorSigma[1, n]; f2[x_] := DivisorSigma[2, x] Table[Max[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
%t A082066 (* Second program: *)
%t A082066 Table[Last[Apply[Intersection, FactorInteger[Map[DivisorSigma[#, n] &, {1, 2}]][[All, All, 1]]] /. {} -> {1}], {n, 109}] (* _Michael De Vlieger_, May 22 2017 *)
%o A082066 (PARI) gpf(n)=if(n>1,my(f=factor(n)[,1]);f[#f],1)
%o A082066 a(n)=gpf(gcd(sigma(n),sigma(n,2))) \\ _Charles R Greathouse IV_, Feb 19 2013
%o A082066 (Python)
%o A082066 from sympy import primefactors, gcd, divisor_sigma
%o A082066 def a006530(n): return 1 if n==1 else primefactors(n)[-1]
%o A082066 def a(n): return a006530(gcd(divisor_sigma(n), divisor_sigma(n, 2))) # _Indranil Ghosh_, May 22 2017
%Y A082066 Cf. A006530, A001157, A000203, A082061-A082065.
%K A082066 nonn
%O A082066 1,3
%A A082066 _Labos Elemer_, Apr 07 2003
%E A082066 Changed "was found" to "exists" in definition. - _N. J. A. Sloane_, Jan 29 2022