A073808 Number of common divisors of sigma_1(n) and sigma_2(n).

1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 2, 8, 3, 2, 2, 4, 2, 2, 6, 4, 2, 3, 2, 4, 3, 2, 3, 4, 2, 4, 3, 4, 2, 3, 2, 8, 4, 2, 2, 4, 4, 4, 3, 4, 2, 6, 3, 4, 6, 4, 2, 12, 2, 2, 4, 2, 3, 3, 2, 8, 3, 3, 2, 4, 2, 2, 4, 4, 3, 3, 2, 4, 3, 2, 2, 6, 3, 2, 6, 4, 2, 4, 3, 8, 3, 2, 3, 8, 2, 4, 4, 4, 2, 3, 2, 4

Offset: 1

Author

Labos Elemer, Aug 13 2002

Keywords

• nonn

Comments

a(n) = Card[Intersection[D[A000203(n)], D[A001157(n)]]]. - This is the formula given by the original author. D[x] here means the set of divisors of x. - Antti Karttunen, Nov 23 2017

Examples

			n=10: sigma[1,10]=18, sigma[1,10]=130 Intersection[{1,2,3,6,9,18},{1,2,5,10,13,26,65,130}]={1,2}, so a(10)=2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000005, A000203, A001157, A073802, A073809.

Programs

Mathematica

g1[x_] := Divisors[DivisorSigma[1, x]] g2[x_] := Divisors[DivisorSigma[2, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
(* Second program: *)
Table[Length@ Apply[Intersection, Divisors@ Array[DivisorSigma[#, n] &, 2]], {n, 105}] (* Michael De Vlieger, Nov 23 2017 *)

PARI

A073808(n) = numdiv(gcd(sigma(n),sigma(n,2))); \\ Antti Karttunen, Nov 23 2017

Formula

a(n) = A000005(gcd(A000203(n), A001157(n))). - Antti Karttunen, Nov 23 2017