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

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%I A073812 #16 Jun 01 2022 17:45:17
%S A073812 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,
%T A073812 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,
%U A073812 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
%N A073812 Number of common divisors of sigma(n) and phi(n).
%H A073812 Amiram Eldar, <a href="/A073812/b073812.txt">Table of n, a(n) for n = 1..10000</a>
%F A073812 a(n) = Card[Intersection[D[A000203(n)], D[A000010(n)]]].
%e A073812 n=36: sigma(36)=91; phi(36)=12; Intersection[{1,7,13,91},{1,2,3,4,6,12}]={1}, so a(36)=1.
%t A073812 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}]
%t A073812 a[n_] := DivisorSigma[0, GCD[DivisorSigma[1, n], EulerPhi[n]]]; Array[a, 100] (* _Amiram Eldar_, Oct 18 2019 *)
%Y A073812 Cf. A000010, A000203, A073802, A073808, A073809, A073810, A073811.
%K A073812 nonn,easy
%O A073812 1,3
%A A073812 _Labos Elemer_, Aug 13 2002