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A073810 Number of common divisors of sigma(2,n) and sigma(3,n). 2
1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 4, 2, 2, 3, 2, 2, 1, 2, 8, 3, 2, 2, 4, 1, 2, 6, 2, 2, 3, 2, 2, 3, 2, 3, 1, 2, 4, 3, 8, 2, 3, 2, 4, 4, 2, 2, 4, 2, 2, 3, 4, 2, 6, 3, 4, 6, 4, 2, 12, 2, 2, 2, 2, 3, 3, 2, 8, 3, 3, 2, 4, 2, 2, 4, 4, 3, 3, 2, 4, 3, 2, 2, 6, 6, 2, 6, 4, 2, 4, 3, 4, 3, 2, 3, 8, 2, 2, 2, 1, 2, 3, 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[A001157(n)], D[A001158(n)]]].

EXAMPLE

n=10: sigma(2,10)=130, sigma(3,10)=1134; Intersection[{{1,2,5,10,13,26,65,130}, {1,2,3,6,7,9,14,18,21,27,42,54,63,81, 126,162,189,378,567,1134}]={1,2}, so a(10)=2.

MATHEMATICA

g1[x_] := Divisors[DivisorSigma[2, x]] g2[x_] := Divisors[DivisorSigma[3, x]] ncd[x_] := Length[Intersection[g1[x], g2[x]]] Table[ncd[w], {w, 1, 128}]

a[n_] := DivisorSigma[0, GCD[DivisorSigma[2, n], DivisorSigma[3, n]]]; Array[a, 100] (* Amiram Eldar, Oct 18 2019 *)

CROSSREFS

Cf. A001157, A001158, A073802, A073808, A073809.

Sequence in context: A163367 A057226 A224963 * A055255 A057768 A317990

Adjacent sequences:  A073807 A073808 A073809 * A073811 A073812 A073813

KEYWORD

nonn,easy

AUTHOR

Labos Elemer, Aug 13 2002

STATUS

approved

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Last modified June 5 15:37 EDT 2020. Contains 334852 sequences. (Running on oeis4.)