SumPrimeDivisors[n_] := Total[First /@ FactorInteger[n]]
RuthAaron[n_] := SumPrimeDivisors[n] == SumPrimeDivisors[n + 1]

SumPrimeFactors[n_] :=
 Total[First[#] * Last[#] & /@ FactorInteger[n]]
RuthAaronFactors[n_] :=
  SumPrimeFactors[n] == SumPrimeFactors[n + 1]

RuthAaronSeq := Select[Range[100000], RuthAaron]
RuthAaronFactorSeq := Select[Range[100000], RuthAaronFactors]

Print["30 Ruth Aaron numbers:"]
Print[Take[RuthAaronSeq, 30]]

Print["\n30 Ruth Aaron factor numbers:"]
Print[Take[RuthAaronFactorSeq, 30]]