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 A241006 Number of positive numbers
 1, 1, 2, 1, 3, 1, 4, 3, 2, 2, 5, 3, 5, 4, 9, 2, 4, 5, 6, 6, 6, 6, 10, 5, 8, 6, 5, 8, 8, 9, 12, 7, 10, 7, 12, 9, 8, 9, 13, 13, 9, 9, 14, 10, 11, 10, 18, 13, 13, 16, 12, 12, 18, 13, 18, 13, 13, 14, 12, 17, 16, 15, 41, 15, 16, 14, 18, 22, 15, 18, 16, 16, 22, 20, 24, 15, 19, 25, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Note that a different sequence could be defined by "Number of positive numbers < n that do not have any anti-divisor as a factor," which gives A066452. Consider for example n=10 with anti-divisors {3,4,7} and the number 2. 2 is not coprime to the anti-divisor 4 and does not contribute to a(10), whereas 2 does not have 4 as a factor and contributes to A066452. LINKS Table of n, a(n) for n=2..80. EXAMPLE 10 has anti-divisors {3,4,7}. The positive integers that are <10 and coprime to all of them are {1,5}, so a(10)=2. The integers 2, 3, 4, 6, 7, 8 and 9 are not coprime to all of {3,4,7} and do not contribute to the count. MAPLE A241006 :=proc(n) local a, ad, i, isco ; a := 0 ; ad := antidivisors(n) ; # implemented in A066272 for i from 1 to n-1 do isco := true; for adiv in ad do if igcd(adiv, i) > 1 then isco := false; break; end if; end do: if isco then a := a+1 ; end if; end do: a ; end proc: CROSSREFS Cf. A066452. Sequence in context: A233204 A308058 A118487 * A249148 A091420 A323906 Adjacent sequences: A241003 A241004 A241005 * A241007 A241008 A241009 KEYWORD nonn AUTHOR R. J. Mathar, Aug 07 2014 STATUS approved

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Last modified November 29 07:03 EST 2023. Contains 367429 sequences. (Running on oeis4.)