cp's OEIS Frontend

A241006 Number of positive numbers that are coprime to all anti-divisors of n.

%I A241006 #10 Aug 07 2014 10:42:03
%S A241006 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 A241006 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 A241006 12,17,16,15,41,15,16,14,18,22,15,18,16,16,22,20,24,15,19,25,21
%N A241006 Number of positive numbers <n that are coprime to all anti-divisors of n.
%C A241006 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.
%e A241006 10 has anti-divisors {3,4,7}. The positive integers that are <10 and coprime to
%e A241006 all of them are {1,5}, so a(10)=2. The integers 2, 3, 4, 6, 7, 8 and 9
%e A241006 are not coprime to all of {3,4,7} and do not contribute to the count.
%p A241006 A241006 :=proc(n)
%p A241006     local a,ad,i,isco ;
%p A241006     a := 0 ;
%p A241006     ad := antidivisors(n) ; # implemented in A066272
%p A241006     for i from 1 to n-1 do
%p A241006         isco := true;
%p A241006         for adiv in ad do
%p A241006             if igcd(adiv,i) > 1 then
%p A241006                 isco := false;
%p A241006                 break;
%p A241006             end if;
%p A241006         end do:
%p A241006         if isco then
%p A241006             a := a+1 ;
%p A241006         end if;
%p A241006     end do:
%p A241006     a ;
%p A241006 end proc:
%Y A241006 Cf. A066452.
%K A241006 nonn
%O A241006 2,3
%A A241006 _R. J. Mathar_, Aug 07 2014