A075655 - OEIS

%I #15 Aug 23 2019 12:41:40

%S 3,24,1088,4224,16640,66048,16785408,67125248,268468224

%N Numbers n such that n + product of prime factors of n = (n+1) + product of prime factors of (n+1).

%C Numbers n such that A073353(n) = A073353(n+1). - _Michel Marcus_, Aug 23 2019

%C No more terms below 10^10. - _Amiram Eldar_, Aug 23 2019

%e 24 + product of prime factors of 24 = 24 + 2 * 3 = 30; 25 + product of prime factors of 25 = 25 + 5 = 30; hence 24 belongs to the sequence.

%t s[n_] := n + Apply[Times, Transpose[FactorInteger[n]][[1]]]; Select[Range[2, 10^5], s[ # ] == s[ # + 1] &]

%t Flatten[Position[Partition[Table[n+Times@@Transpose[FactorInteger[ n]] [[1]],{n,2,100000}],2,1],_?(#[[1]]==#[[2]]&),{1},Heads->False]]+1 (* _Harvey P. Dale_, Apr 20 2014 *)

%t rad[n_] := Times @@ First /@ FactorInteger[n]; r1 = 1; s = {}; Do[r2 = rad[n]; If[r1 - r2 == 1, AppendTo[s, n-1]]; r1 = r2, {n, 2, 10^5}]; s (* _Amiram Eldar_, Aug 23 2019 *)

%Y Cf. A007947, A073353, A081083, A081084.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 12 2002

%E a(7)-a(9) from _Amiram Eldar_, Aug 23 2019