A073812 Number of common divisors of sigma(n) and phi(n).

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

Offset

1,3

Links

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

Formula

a(n) = Card[Intersection[D[A000203(n)], D[A000010(n)]]].

Example

n=36: sigma(36)=91; phi(36)=12; Intersection[{1,7,13,91},{1,2,3,4,6,12}]={1}, so a(36)=1.

Mathematica

g1[x_] := Divisors[DivisorSigma[1, x]] g2[x_] := Divisors[EulerPhi[x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]
a[n_] := DivisorSigma[0, GCD[DivisorSigma[1, n], EulerPhi[n]]]; Array[a, 100] (* Amiram Eldar, Oct 18 2019 *)

Crossrefs

Cf. A000010, A000203, A073802, A073808, A073809, A073810, A073811.

Sequence in context: A336476 A082064 A082055 * A009223 A110244 A309020

Adjacent sequences: A073809 A073810 A073811 * A073813 A073814 A073815

Keyword

nonn,easy

Author

Labos Elemer, Aug 13 2002

Status

approved