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
Examples
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
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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
Links
- David A. Corneth, Table of n, a(n) for n = 1..10000
- David A. Corneth, PARI program
Crossrefs
Programs
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Mathematica
Table[Length[Select[Range[n],PrimeNu[#]
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PARI
\\ See Corneth link