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

1,1

Comments

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

Lü & Wang (following a number of others) prove that this sequence has lower density at least 0.2017 and upper density at most 0.7983. - Charles R Greathouse IV, Mar 11 2026

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

Xiaodong Lü and Zhiwei Wang, On the largest prime factors of consecutive integers, 2018.

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 *)

Crossrefs

Cf. A006530, A070089.

Sequence in context: A245644 A371168 A370811 * A383612 A343011 A100933

Adjacent sequences: A070084 A070085 A070086 * A070088 A070089 A070090

Keyword

nonn

Author

N. J. A. Sloane, May 13 2002

Status

approved