A067712 Numbers n such that sum of exponents in prime factorization of n is > log(n).

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

Offset: 1

Author

Leroy Quet, Feb 05 2002

Keywords

• easy
• nonn

Examples

			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).
		

References

• Conway, John H. and Guy, Richard K., The Book of Numbers, Copernicus, 1996, pp. 132-133.
• Ore, Oystein, Number Theory and Its History, McGraw-Hill, 1948, (also reprinted 1988), pp. 50-52.

Crossrefs

Cf. A067715, A081209.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Walter Nissen, Mar 10 2003