Re: Implementation of functions for "Integer partitions detect the primes" paper

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Wed, Jul 09, 2025 at 10:00:15PM +0200, hermann@stamm-wilbrandt.de wrote:
> On 2025-07-08 22:09, Bill Allombert wrote:
> > You should do
> > M1(n)=my(s=0);fordiv(n,d,s+=d);s;
> > 
> > But this function is just sigma(n)
> > 
> Ok.
> 
> > > ? M2(n)=s=0;for(m=1,n,forpart(v=m,if(v[1]<v[2],for(d=1,n\v[1],r=n-d*v[1];if(r%v[2]==0,s+=d*(r\v[2])))),[1,m],[2,2]));s;
> > 
> > As I understand this function is
> > (sigma(n,3)-(2*n-1)*sigma(n))/8
> > which is much faster to compute.
> > 
> That does not work:
> 
> ? M1(n)=sigma(n);
> ? M2(n)=(sigma(n,3)-(2*n-1)*sigma(n))/8;
> ? T1(n)=(n^2 - 3^n + 2)*M1(n) - 8*M2(n);
                 ^^^
This should be 3*n.

Cheers,
Bill