A322837 Number of positive integers less than n with fewer distinct prime factors than n.

0, 1, 1, 1, 1, 5, 1, 1, 1, 8, 1, 9, 1, 10, 10, 1, 1, 12, 1, 13, 13, 13, 1, 14, 1, 15, 1, 16, 1, 29, 1, 1, 19, 19, 19, 19, 1, 20, 20, 20, 1, 40, 1, 22, 22, 22, 1, 23, 1, 24, 24, 24, 1, 25, 25, 25, 25, 25, 1, 57, 1, 27, 27, 1, 28, 62, 1, 29, 29, 65, 1, 30, 1, 31

Offset

1,6

Links

Table of n, a(n) for n=1..74.

Example

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

Mathematica

Table[Length[Select[Range[n], PrimeNu[#]<PrimeNu[n]&]], {n, 100}]

Crossrefs

Positions of 1's are A246655.

Cf. A000010, A001221, A006049, A067003, A294277, A294278, A302242, A322838, A322841.

Sequence in context: A367202 A292771 A369364 * A348978 A168677 A345939

Adjacent sequences: A322834 A322835 A322836 * A322838 A322839 A322840

Keyword

nonn

Author

Gus Wiseman, Dec 28 2018

Status

approved