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A067003
Number of numbers <= n with same number of distinct prime factors as n.
10
1, 1, 2, 3, 4, 1, 5, 6, 7, 2, 8, 3, 9, 4, 5, 10, 11, 6, 12, 7, 8, 9, 13, 10, 14, 11, 15, 12, 16, 1, 17, 18, 13, 14, 15, 16, 19, 17, 18, 19, 20, 2, 21, 20, 21, 22, 22, 23, 23, 24, 25, 26, 24, 27, 28, 29, 30, 31, 25, 3, 26, 32, 33, 27, 34, 4, 28, 35, 36, 5, 29, 37, 30, 38, 39, 40, 41
OFFSET
1,3
LINKS
FORMULA
a(A002110(n)) = 1.
EXAMPLE
a(11)=8 since 2,3,4,5,7,8,9,11 each have one distinct prime factor. a(12)=3 since 6,10,12 each have two distinct prime factors.
From Gus Wiseman, Dec 28 2018: (Start)
Column n lists the a(n) positive integers less than or equal to n with the same number of distinct prime factors as n:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
---------------------------------------------------------------------
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 3 4 5 7 8 6 9 10 11 12 14 13 16 15 17 18
2 3 4 5 7 8 6 9 10 12 11 13 14 16 15
2 3 4 5 7 8 6 10 9 11 12 13 14
2 3 4 5 7 6 8 9 10 11 12
2 3 4 5 7 8 6 9 10
2 3 4 5 7 8 6
2 3 4 5 7
2 3 4 5
2 3 4
2 3
2
(End)
MATHEMATICA
Table[Length[Select[Range[n], PrimeNu[#]==PrimeNu[n]&]], {n, 100}] (* Gus Wiseman, Dec 28 2018 *)
PROG
(PARI) a(n) = my(nb = #factor(n)~); sum(k=1, n, #factor(k)~ == nb); \\ Michel Marcus, Jul 13 2019
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Henry Bottomley, Dec 21 2001
STATUS
approved