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A073810
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Number of common divisors of sigma(2,n) and sigma(3,n).
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3
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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
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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