[GAP Forum] [group-pub-forum] Arithmetic GAP code

[Stefan Kohl]

I think the following functions should serve your purpose:

     TauPrime := n -> Product(List(Collected(Factors(n)),p->Tau(p[2])));

     SigmaPrime := n -> 
Product(List(Collected(Factors(n)),p->Sum(DivisorsInt(p[2]),d->p[1]^d)));

Does this help you?

Best regards,

      Stefan

P.S.: Questions about GAP are best sent to the GAP Forum.

Am 28.10.2017 um 12:57 schrieb lopo apelo kosho:
> Dear Friends,
> Consider n=p_1^a1⋯p_r^ar. An integer d=p_i^bi⋯p_r^br is called an 
> /exponential divisor/ of n if b_i divides  a_i for every 1≤i≤r.
> I am trying to write a GAP code to compute the  two functions: τ′(n), 
> the number of exponential divisors of n, and σ′(n), the sum of the 
> exponential divisors of n.
> Both τ′ and σ′ are multiplicative, hence we only need to look at them 
> on prime powers. For example
> σ′(p^6)=p+p^2+p^3+p^6,
> and
> τ′(p^6)=4.
> Thank you.