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A066929 Numbers n such that Omega(n) = floor(log(n)). 1

%I

%S 1,3,5,7,9,10,14,15,27,28,30,42,44,45,50,52,56,60,81,84,88,90,100,104,

%T 126,132,135,136,140,162,168,176,180,200,208,243,252,264,270,272,280,

%U 300,304,312,368,378,392,396,416,486,504,528,540,544,560,600,608,624

%N Numbers n such that Omega(n) = floor(log(n)).

%C Since e < 3, one can prove that a(n) is even for large enough n; in particular if n > 370 then a(n) is even, if n > 1568 then a(n) is divisible by 4, and so forth. Generally, if k > 2^m * 3^floor(((1 - log 2)m + log 2)/(log 3 - 1)) is in this sequence then 2^m divides k. - _Charles R Greathouse IV_, Sep 04 2015

%H Harry J. Smith, <a href="/A066929/b066929.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 300 = 2^2 * 3 * 5^2, floor(log(300)) = 5 = 2 + 1 + 2, hence 300 is in the sequence.

%t Select[Range[10^4],PrimeOmega[#]==Floor[Log[#]]&] (* _Enrique PĂ©rez Herrero_, Jan 08 2013 *)

%o (PARI) n=0; for (m=1, 10^10, if (bigomega(m) == floor(log(m)), write("b066929.txt", n++, " ", m); if (n==1000, return)) ) \\ _Harry J. Smith_, Apr 07 2010

%o (PARI) is(n)=bigomega(n)==log(n)\1 \\ _Charles R Greathouse IV_, Sep 04 2015

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jan 23 2002

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Last modified August 5 08:48 EDT 2021. Contains 346464 sequences. (Running on oeis4.)