[GAP Forum] [group-pub-forum] Arithmetic GAP code
Stefan Kohl
sk239 at st-andrews.ac.uk
Sat Oct 28 13:29:00 BST 2017
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.
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