

A005236


Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n.
(Formerly M0501)


3



2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 17, 18, 20, 24, 26, 28, 30, 33, 38, 42, 48, 50, 54, 60, 65, 74, 82, 84, 90, 98, 102, 108, 110, 114, 126, 129, 138, 150, 164, 168, 174, 180, 194, 198, 228, 234, 244, 252, 258, 264, 270, 290, 294, 318, 348, 354, 360, 384, 390, 402
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OFFSET

1,1


COMMENTS

omega(m) is the number of distinct prime factors of m.


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B8.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Paul Erdos, Some Unconventional Problems in Number Theory, Mathematics Magazine, Vol. 52, No. 2, Mar., 1979, pp. 6770. See Problem 4. p. 68.
Paul Erdos, Some unconventional problems in number theory, Acta Mathematica Hungarica, 33(1):7180, 1979.


EXAMPLE

1 + omega(1) = 1, 2 + omega(2) = 3, 3 + omega(3) = 4, 4 + omega(4) = 5, 5 + omega(5) = 6.
Thus we have verified that m + omega(m) < 6 for m < 6, so 6 is in the sequence.
But since 6 + omega(6) = 8 > 7, 7 is not in the sequence.


MATHEMATICA

omegaBarrierQ[n_] := (For[m = 1, m < n, m++, If[m + PrimeNu[m] > n, Return[False]]]; True); Select[Range[2, 500], omegaBarrierQ] (* JeanFrançois Alcover, Feb 03 2015 *)


PROG

(PARI) is(n)=for(k=1, log(n)\log(5), if(omega(nk)>k, return(0))); n>1 \\ Charles R Greathouse IV, Sep 19 2012
(Haskell)
a005236 n = a005236_list !! (n1)
a005236_list = filter (\x > all (<= x) $ map a229109 [1..x1]) [2..]
 Reinhard Zumkeller, Sep 13 2013


CROSSREFS

Cf. A001221, A229109.
Sequence in context: A164043 A172248 A082415 * A051250 A143071 A305759
Adjacent sequences: A005233 A005234 A005235 * A005237 A005238 A005239


KEYWORD

nonn,nice,changed


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from John W. Layman


STATUS

approved



