DEDEKIND's PSI FUNCTION
\[\psi (n)\]
$$\psi ~~~~ psi $$
\[\psi_{Dedekind}(n)=n~\prod_{p|n}^{ }(1+\frac{1}{p})\]
#Dedekind's Psi function
def dedekind_psi(n) :
d_psi = n * prod([1 + 1/p for p in prime_divisors(n)])
return d_psi
dedekind_psi(2)
[dedekind_psi(n) for n in [1..10]]
A001615 Dedekind's psi function.
1,3,4,6,6,12,8,12,12,18,12,24,14,24,24,24,18,36,20,36,32,36,24
Generalization of Dedekind Psi Function : \[D_{k}(n)=n^{k}~\prod_{p|n}^{ }(1+\frac{1}{p^{k}})\]
#Generalized Dedekind's Psi function
def dedekind_psi_g(k, n) :
d_psi_g = n^k * prod([1 + 1/p^k for p in prime_divisors(n)])
return d_psi_g
dedekind_psi_g(2, 25)
[dedekind_psi_g(2, n) for n in [1..10]]
A065958 Generalised Dedekind function D_2(n)
1,5,10,20,26,50,50,80,90,130,122,200,170,250,260,320,290,450,362,520