

A067712


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


2



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



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



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



