This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082054 #13 Feb 16 2025 05:39:49
%S A082054 0,0,2,0,2,2,2,0,0,2,2,2,2,5,2,0,2,3,2,2,2,2,2,2,0,5,2,2,2,2,2,0,2,2,
%T A082054 5,0,2,5,2,2,2,5,2,2,5,2,2,2,3,0,2,2,2,5,2,5,2,2,2,2,2,5,2,0,5,2,2,2,
%U A082054 2,5,2,3,2,5,2,2,5,5,2,2,0,2,2,2,2,5,2,7,2,5,2,2,2,2,5,2,2,3,5,0,2,2,2,5,5
%N A082054 Sum of common prime divisors (without multiplicity) of sigma(n) and phi(n).
%H A082054 Charles R Greathouse IV, <a href="/A082054/b082054.txt">Table of n, a(n) for n = 1..10000</a>
%F A082054 a(n) = A008472(A009223(n)). - _Amiram Eldar_, Feb 16 2025
%t A082054 ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; Table[Apply[Plus, Intersection[ba[EulerPhi[w]], ba[DivisorSigma[1, w]]]], {w, 1, 256}]
%t A082054 a[n_] := Module[{g = GCD[DivisorSigma[1, n], EulerPhi[n]]}, If[g == 1, 0, Total[FactorInteger[g][[;; , 1]]]]]; Array[a, 100] (* _Amiram Eldar_, Feb 16 2025 *)
%o A082054 (PARI) a(n)=my(f=factor(gcd(sigma(n=factor(n)), eulerphi(n)))[,1]); sum(i=1,#f,f[i]) \\ _Charles R Greathouse IV_, Dec 09 2013
%Y A082054 Cf. A000010, A000203, A008472, A009223.
%K A082054 nonn
%O A082054 1,3
%A A082054 _Labos Elemer_, Apr 03 2003