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

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

2,3

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