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A070089 P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n. 9
1, 2, 4, 6, 8, 9, 10, 12, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 57, 58, 60, 64, 66, 68, 70, 72, 75, 77, 78, 81, 82, 84, 85, 88, 90, 91, 92, 93, 96, 98, 100, 102, 105, 106, 108, 110, 112, 114, 115, 117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

There are 500149 terms in this sequence up to 10^6, 4999951 up to 10^7, 49997566 up to 10^8, and 499992458 up to 10^9. With a binomial model with p = 1/2, these would be +0.3, -0.5, -0.0, and -0.5 standard deviations from their respective means. In other words, Erdős's conjecture seems solid. - Charles R Greathouse IV, Oct 27 2015

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

MATHEMATICA

f[n_] := FactorInteger[n][[ -1, 1]]; Select[ Range[125], f[ # ] < f[ # + 1] &]

PROG

(PARI) gpf(n)=if(n<3, n, my(f=factor(n)[, 1]); f[#f])

is(n)=gpf(n) < gpf(n+1) \\ Charles R Greathouse IV, Oct 27 2015

CROSSREFS

Cf. A006530, A070087.

Sequence in context: A176693 A118672 A100417 * A069167 A217352 A036627

Adjacent sequences:  A070086 A070087 A070088 * A070090 A070091 A070092

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 13 2002

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.