A075655 Numbers n such that n + product of prime factors of n = (n+1) + product of prime factors of (n+1).

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

Offset

1,1

Comments

Numbers n such that A073353(n) = A073353(n+1). - Michel Marcus, Aug 23 2019

No more terms below 10^10. - Amiram Eldar, Aug 23 2019

Links

Table of n, a(n) for n=1..9.

Example

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.

Mathematica

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

Crossrefs

Cf. A007947, A073353, A081083, A081084.

Sequence in context: A277177 A226053 A233894 * A300551 A000856 A242117

Adjacent sequences: A075652 A075653 A075654 * A075656 A075657 A075658

Keyword

nonn

Author

Joseph L. Pe, Oct 12 2002

Extensions

a(7)-a(9) from Amiram Eldar, Aug 23 2019

Status

approved