A082417 Numbers k such that P(k) < P(k+1) > P(k+2), where P(k) is the largest prime factor of k (A006530).

2, 4, 6, 10, 12, 16, 18, 22, 25, 28, 30, 33, 36, 40, 42, 46, 48, 50, 52, 54, 58, 60, 64, 66, 68, 70, 72, 75, 78, 82, 85, 88, 93, 96, 98, 100, 102, 106, 108, 110, 112, 115, 117, 121, 126, 128, 130, 133, 136, 138, 141, 145, 148, 150, 154, 156, 160, 162, 166, 172, 178, 180, 182

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, A082418-A082422, A071869, A071870, A100392.

Programs

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]]; ind = Position[Differences[Array[gpf, 200]], ?(# > 0 &)] // Flatten; ind[[Position[Differences[ind], ?(# > 1 &)] // Flatten]] (* Amiram Eldar, Jun 06 2022 *)

Formula

a(n) = A100392(n) - 1. - T. D. Noe, Nov 26 2007