

A241006


Number of positive numbers <n that are coprime to all antidivisors of n.


1



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
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OFFSET

2,3


COMMENTS

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.


LINKS



EXAMPLE

10 has antidivisors {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

local a, ad, i, isco ;
a := 0 ;
ad := antidivisors(n) ; # implemented in A066272
for i from 1 to n1 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



KEYWORD

nonn


AUTHOR



STATUS

approved



