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A073812 Number of common divisors of sigma(n) and phi(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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, A0738010, A073811.

Sequence in context: A123926 A082064 A082055 * A009223 A110244 A309020

Adjacent sequences:  A073809 A073810 A073811 * A073813 A073814 A073815

KEYWORD

nonn,easy

AUTHOR

Labos Elemer, Aug 13 2002

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)