Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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,changed
%O 1,3
%A _Labos Elemer_, Aug 13 2002