A322837 - OEIS

%I #14 Sep 17 2024 08:11:39

%S 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,

%T 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,

%U 25,25,25,25,1,57,1,27,27,1,28,62,1,29,29,65,1,30,1,31

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

%H David A. Corneth, <a href="/A322837/b322837.txt">Table of n, a(n) for n = 1..10000</a>

%H David A. Corneth, <a href="/A322837/a322837.gp.txt">PARI program</a>

%e Column n lists the a(n) positive integers less than n with fewer distinct prime factors than n:

%e   1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20

%e   ---------------------------------------------------------------------

%e      1  1  1  1  5  1  1  1  9   1   11  1   13  13  1   1   17  1   19

%e                  4           8       9       11  11          16      17

%e                  3           7       8       9   9           13      16

%e                  2           5       7       8   8           11      13

%e                  1           4       5       7   7           9       11

%e                              3       4       5   5           8       9

%e                              2       3       4   4           7       8

%e                              1       2       3   3           5       7

%e                                      1       2   2           4       5

%e                                              1   1           3       4

%e                                                              2       3

%e                                                              1       2

%e                                                                      1

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

%o (PARI) \\ See Corneth link

%Y Positions of 1's are A246655.

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

%K nonn,easy

%O 1,6

%A _Gus Wiseman_, Dec 28 2018