A073810 Number of common divisors of sigma(2,n) and sigma(3,n).

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, 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, 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

Offset: 1

Author

Labos Elemer, Aug 13 2002

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001157, A001158, A073802, A073808, A073809.

Programs

Mathematica

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}]
a[n_] := DivisorSigma[0, GCD[DivisorSigma[2, n], DivisorSigma[3, n]]]; Array[a, 100] (* Amiram Eldar, Oct 18 2019 *)

Formula

a(n) = Card[Intersection[D[A001157(n)], D[A001158(n)]]].