# Sum Over Coprime Integers = 0 (or 1)

Michele Dondi blazar at pcteor1.mi.infn.it
Fri Sep 24 11:27:18 CEST 2004

```NOTE: this is *not* a mistake!

On Tue, 10 Aug 2004, Leroy Quet wrote:

>> a(1) = 1;
>>
>> For each m >= 3,
>>
>> 0 = sum{1<=k<m,GCD(k,m)=1} a(k).
[snip]
> I just posted the following to the EIS, with more terms calculated
> (correctly??).
>
> %I A000001
> %S A000001 1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,3,-3,-1,1,-3

I get

1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 3, -3, -1, 1, -3, 3, 1, -1, 1,
-1, -1, -1, 5, -1, -1, -1, -1, 1, -1, 1, -3, 5, -3, 1, 7, -5, -1, -1, -9,
9, 5, 3, 3, -11, -3, 7, 7, 9, -1, -19, -7, 17, 11, 9, -7, -23, 1, -1, -1,
37, 1, -33, -1, -3, -3, 15, 27, -39, -7, 7, -9, 47, -13, -37, 11, 1, -5,
51, -9, -37, 19, 17, -5, -1, 13, -43, -5, -3, 13, 95, -29, -107, -19, 55,
53, 17, -55, -15

with the following perl program:

#!/usr/bin/perl -l

use strict;
use warnings;

sub gcd {
my (\$n,\$m)=@_;
\$m ? gcd(\$m,\$n%\$m) : \$n;
}

my @a=(0,1);

\$,=', ';

print \$a[1], map {
my (\$n,\$m) = (\$_,\$_+1);
\$a[\$n]=do {
my \$t;
\$t+=\$a[\$_] for
grep gcd(\$m,\$_)==1, 1..\$n-1;
-\$t;
}
} 2..100;

__END__

I have the *impression* of having already seen this sequence, but cannot
tell for sure...

Michele
--
> Di solito vedo persone come te svenute nelle taverne.
Ancor PRIMA che ti sentano l'alito?
- "Cavaliere Verde" su it.discussioni.litigi

```