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

Offset: 2

Author

R. J. Mathar, Aug 07 2014

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A066452.

Programs

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: