%I #19 Jan 10 2025 02:38:40
%S 1,1,2,1,2,2,2,2,1,2,2,4,2,2,3,2,2,1,2,8,3,2,2,4,1,2,6,2,2,3,2,2,3,2,
%T 3,1,2,4,3,8,2,3,2,4,4,2,2,4,2,2,3,4,2,6,3,4,6,4,2,12,2,2,2,2,3,3,2,8,
%U 3,3,2,4,2,2,4,4,3,3,2,4,3,2,2,6,6,2,6,4,2,4,3,4,3,2,3,8,2,2,2,1,2,3,2,4
%N Number of common divisors of sigma(2,n) and sigma(3,n).
%H Amiram Eldar, <a href="/A073810/b073810.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Card[Intersection[D[A001157(n)], D[A001158(n)]]].
%e n=10: sigma(2,10)=130, sigma(3,10)=1134; Intersection[{1,2,5,10,13,26,65,130}, {1,2,3,6,7,9,14,18,21,27,42,54,63,81, 126,162,189,378,567,1134}]={1,2}, so a(10)=2.
%t g1[x_] := Divisors[DivisorSigma[2, x]] g2[x_] := Divisors[DivisorSigma[3, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
%t a[n_] := DivisorSigma[0, GCD[DivisorSigma[2, n], DivisorSigma[3, n]]]; Array[a, 100] (* _Amiram Eldar_, Oct 18 2019 *)
%Y Cf. A001157, A001158, A073802, A073808, A073809.
%K nonn,easy
%O 1,3
%A _Labos Elemer_, Aug 13 2002