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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