A322838 Number of positive integers less than n with more prime factors than n, counted with multiplicity.

0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 5, 0, 6, 2, 2, 0, 9, 1, 10, 1, 5, 5, 13, 0, 6, 6, 2, 2, 18, 2, 19, 0, 10, 10, 10, 1, 24, 11, 11, 1, 27, 5, 28, 5, 5, 15, 31, 0, 16, 6, 17, 6, 36, 2, 19, 2, 20, 20, 41, 2, 42, 21, 9, 0, 23, 10, 47, 10, 25, 10, 50, 1, 51, 27, 11, 11

Offset: 1

Author

Gus Wiseman, Dec 28 2018

Keywords

• nonn

Examples

			Column n lists the a(n) positive integers less than n with more prime factors than n:
  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20
  ---------------------------------------------------------------------
              4     6     8  8   10      12  12  12      16  16  18  16
                    4            9       10  8   8       15      16
                                 8       9               14      15
                                 6       8               12      14
                                 4       6               10      12
                                         4               9       10
                                                         8       9
                                                         6       8
                                                         4       6
                                                                 4
		

Crossrefs

Positions of zeros appear to be A029744.

Cf. A000010, A000961, A001221, A001222, A045920, A058933, A061142, A067003, A302242, A322839, A322841.

Programs

Mathematica

Table[Length[Select[Range[n],PrimeOmega[#]>PrimeOmega[n]&]],{n,100}]