A067712 - OEIS

%I #23 Feb 01 2024 18:25:07

%S 2,4,6,8,12,16,18,20,24,32,36,40,48,54,64,72,80,96,108,112,120,128,

%T 144,160,192,216,224,240,256,288,320,324,336,352,360,384,400,432,448,

%U 480,512,576,640,648,672,704,720,768,800,832,864,896,960,972,1008,1024,1056

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

%D Conway, John H. and Guy, Richard K., The Book of Numbers, Copernicus, 1996, pp. 132-133.

%D Ore, Oystein, Number Theory and Its History, McGraw-Hill, 1948, (also reprinted 1988), pp. 50-52.

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

%e a(1) = 2 because 2 has 1 prime factor, viz., 2 and log(2) ~= 0.693 and 1 > 0.693.

%e 4 is included because sum of exponents in prime factorization of 4 is 2, which is > log(4).

%t Select[Range[2,1100],Total[FactorInteger[#][[All,2]]]>Log[#]&] (* _Harvey P. Dale_, Feb 04 2019 *)

%Y Cf. A067715, A081209.

%K easy,nonn

%O 1,1

%A _Leroy Quet_, Feb 05 2002

%E More terms from _Walter Nissen_, Mar 10 2003