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A076533
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Numbers n such that sum of the distinct prime factors of phi(n) = sum of the distinct prime factors of sigma(n).
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10
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1, 3, 14, 35, 42, 70, 105, 119, 209, 210, 238, 248, 297, 357, 412, 418, 477, 594, 595, 616, 627, 714, 744, 954, 1045, 1142, 1178, 1190, 1236, 1240, 1254, 1328, 1339, 1463, 1485, 1672, 1674, 1703, 1736, 1785, 1848, 1863, 2079, 2090, 2376, 2385, 2540, 2728
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OFFSET
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1,2
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LINKS
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EXAMPLE
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sopf(sigma(14)) = 5; sopf(phi(14))) = 5; hence 14 is a term of the sequence.
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MATHEMATICA
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p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[DivisorSigma[1, # ]] == p[EulerPhi[ # ]] &]
Select[Range[3000], Total[FactorInteger[DivisorSigma[1, #]][[All, 1]]] == Total[ FactorInteger[EulerPhi[#]][[All, 1]]]&] (* Harvey P. Dale, Sep 20 2016 *)
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PROG
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(PARI) sopf(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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