%I #10 Aug 07 2014 10:42:03
%S 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,
%T 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,
%U 12,17,16,15,41,15,16,14,18,22,15,18,16,16,22,20,24,15,19,25,21
%N Number of positive numbers <n that are coprime to all antidivisors of n.
%C Note that a different sequence could be defined by "Number of positive numbers < n that do not have any antidivisor as a factor," which gives A066452. Consider for example n=10 with antidivisors {3,4,7} and the number 2. 2 is not coprime to the antidivisor 4 and does not contribute to a(10), whereas 2 does not have 4 as a factor and contributes to A066452.
%e 10 has antidivisors {3,4,7}. The positive integers that are <10 and coprime to
%e all of them are {1,5}, so a(10)=2. The integers 2, 3, 4, 6, 7, 8 and 9
%e are not coprime to all of {3,4,7} and do not contribute to the count.
%p A241006 :=proc(n)
%p local a,ad,i,isco ;
%p a := 0 ;
%p ad := antidivisors(n) ; # implemented in A066272
%p for i from 1 to n1 do
%p isco := true;
%p for adiv in ad do
%p if igcd(adiv,i) > 1 then
%p isco := false;
%p break;
%p end if;
%p end do:
%p if isco then
%p a := a+1 ;
%p end if;
%p end do:
%p a ;
%p end proc:
%Y Cf. A066452.
%K nonn
%O 2,3
%A _R. J. Mathar_, Aug 07 2014
