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
Examples
n=36: sigma(36)=91; phi(36)=12; Intersection[{1,7,13,91},{1,2,3,4,6,12}]={1}, so a(36)=1.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
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 *)