

A067712


Numbers n such that sum of exponents in prime factorization of n is > log(n).


0



2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 48, 54, 64, 72, 80, 96, 108, 112, 120, 128, 144, 160, 192, 216, 224, 240, 256, 288, 320, 324, 336, 352, 360, 384, 400, 432, 448, 480, 512, 576, 640, 648, 672, 704, 720, 768, 800, 832, 864, 896, 960, 972, 1008, 1024, 1056
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OFFSET

1,1


REFERENCES

Conway, John H. and Guy, Richard K., The Book of Numbers, Copernicus, 1996, pp. 132133.
Ore, Oystein, Number Theory and Its History, McGrawHill, 1948, (also reprinted 1988), pp. 5052.


LINKS

Table of n, a(n) for n=1..57.


FORMULA

OMEGA(n) > log(n), where OMEGA is the total number of prime factors.


EXAMPLE

a(1) = 2 because 2 has 1 prime factor, viz., 2 and log(2) ~= 0.693 and 1 > 0.693.
4 is included because sum of exponents in prime factorization of 4 is 2, which is > log(4).


MATHEMATICA

Select[Range[2, 1100], Total[FactorInteger[#][[All, 2]]]>Log[#]&] (* Harvey P. Dale, Feb 04 2019 *)


CROSSREFS

Cf. A081209.
Sequence in context: A320580 A068997 A293928 * A060765 A140110 A128397
Adjacent sequences: A067709 A067710 A067711 * A067713 A067714 A067715


KEYWORD

easy,nonn


AUTHOR

Leroy Quet, Feb 05 2002


EXTENSIONS

More terms from Walter Nissen, Mar 10 2003


STATUS

approved



