A082418 Numbers n such that P(n) > P(n+1) < P(n+2), where P(n) = largest prime factor of n (A006530).

3, 5, 7, 11, 15, 17, 19, 23, 26, 29, 31, 35, 39, 41, 44, 47, 49, 51, 53, 55, 59, 63, 65, 67, 69, 71, 74, 76, 80, 83, 87, 89, 95, 97, 99, 101, 104, 107, 109, 111, 113, 116, 119, 124, 127, 129, 131, 134, 137, 139, 143, 146, 149, 153, 155, 159, 161, 164, 167, 174, 179, 181, 183

Offset: 1

Author

N. J. A. Sloane, Apr 25 2003

Keywords

• nonn

References

• Antal Balog, On the largest prime factor of consecutive integers, Abstracts Amer. Math. Soc., 25 (No. 2, 2002), p. 337, #975-11-76.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• P. Erdős and C. Pomerance, On the largest prime factors of n and n+1, Aequationes Math. 17 (1978), p. 311-321. [alternate link]

Crossrefs

Cf. A006530, A082417-A082422, A071869, A071870.

Programs

Mathematica

Flatten[Position[Partition[Table[FactorInteger[n][[-1,1]],{n,200}],3,1], ?(#[[1]]> #[[2]] <#[[3]]&),{1},Heads->False]] (* _Harvey P. Dale, Jan 10 2016 *)

Formula

a(n) = A100390(n) - 1. - T. D. Noe, Nov 26 2007