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A081383
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Least x = a(n) such that number of common prime factors (ignoring multiplicity) of sigma(x) = A000203(x) and phi(x) = A000010(x) equals n.
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3
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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x = 209: sigma(209) = 240 = 2^4*3*5, phi(209) = 180 = 2^2*3^2*5, common factor set = {2,3,5}, so a(3) = 209.
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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]}] t=Table[0, {10}]; Do[s=Length[Intersection[ba[EulerPhi[n]], ba[DivisorSigma[1, n]]]]; If[s<11&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}]; t
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PROG
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(PARI) a(n)=my(k=prod(i=1, n, prime(i))); while(omega(gcd(sigma(k), eulerphi(k)))!=n, k++); k \\ Charles R Greathouse IV, Feb 14 2013
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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