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

1, 3, 5, 7, 9, 10, 14, 15, 27, 28, 30, 42, 44, 45, 50, 52, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624

Offset

1,2

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

Select[Range[10^4], PrimeOmega[#]==Floor[Log[#]]&] (* Enrique Pérez Herrero, Jan 08 2013 *)

Prog

(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
(PARI) is(n)=bigomega(n)==log(n)\1 \\ Charles R Greathouse IV, Sep 04 2015

Crossrefs

Sequence in context: A187347 A187413 A091177 * A173909 A165249 A098160

Adjacent sequences: A066926 A066927 A066928 * A066930 A066931 A066932

Keyword

nonn

Author

Benoit Cloitre, Jan 23 2002

Status

approved