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

1,3

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A057226 A338260 A224963 * A055255 A057768 A317990

Adjacent sequences: A073807 A073808 A073809 * A073811 A073812 A073813

Keyword

nonn,easy,changed

Author

Labos Elemer, Aug 13 2002

Status

approved