A070087 P(n) > P(n+1) where P(n) (A006530) is the largest prime factor of n.

3, 5, 7, 11, 13, 14, 15, 17, 19, 23, 26, 29, 31, 34, 35, 37, 38, 39, 41, 43, 44, 47, 49, 51, 53, 55, 59, 61, 62, 63, 65, 67, 69, 71, 73, 74, 76, 79, 80, 83, 86, 87, 89, 94, 95, 97, 99, 101, 103, 104, 107, 109, 111, 113, 116, 118, 119, 122, 123, 124

Offset: 1

Author

N. J. A. Sloane, May 13 2002

Keywords

• nonn

Comments

Erdos conjectured that this sequence has asymptotic density 1/2.

References

• H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 210.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A006530, A070089.

Programs

Mathematica

f[n_] := FactorInteger[n][[ -1, 1]]; Select[ Range[125], f[ # ] > f[ # + 1] &]
With[{lpfn=Table[FactorInteger[n][[-1,1]],{n,200}]},Flatten[ Position[ Partition[ lpfn,2,1],?(#[[1]]>#[[2]]&),{1},Heads->False]]] (* _Harvey P. Dale, Sep 14 2014 *)