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A081396
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Number of common prime factors (ignoring multiplicity) of sigma(n)=A000203(n) and phi(n)=A000010(n).
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2
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0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0
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OFFSET
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1,14
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LINKS
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Table of n, a(n) for n=1..100.
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EXAMPLE
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n=209: sigma(209)=240=2.2.2.2.3.5, phi(209)=180=2.2.3.3.5, common-factor-set={2,3,5}, so a(209)=3.
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] Table[Length[Intersection[ba[EulerPhi[w]], ba[DivisorSigma[1, w]]]], {w, 1, 100}]
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PROG
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(PARI) a(n)=omega(gcd(sigma(n), eulerphi(n))) \\ Charles R Greathouse IV, Feb 19 2013
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CROSSREFS
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Cf. A000203, A000010, A081383.
Sequence in context: A052343 A073484 A203947 * A194293 A194297 A100544
Adjacent sequences: A081393 A081394 A081395 * A081397 A081398 A081399
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 28 2003
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STATUS
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approved
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