

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
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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



