Help:=proc(): print(` muList(N) , muListD(N) `): end:

with(numtheory):

#muList(N): inputs a pos. integer N and outputs
#[seq(mu(i),i=1..N)]:
muList:=proc(N) local eq,var,mu,i,j:

var:={seq(mu[i],i=1..N)}:
eq:={mu[1]-1, seq(add(mu[j],j in divisors(i)),i=2..N)}:

var:=solve(eq,var):

[seq(subs(var, mu[j]),j=1..N)]:

end:


#muListD(N): inputs a pos. integer N and outputs
#[seq(mu(i),i in divisors(N) ]:
muListD:=proc(N) local S,eq,var,mu,i,j:
S:=divisors(N):

var:={seq(mu[i],i in S)}:

eq:={mu[1]-1, seq(add(mu[j],j in divisors(i)),i in S minus {1})}:

var:=solve(eq,var):



end:


#Def: good person: Doesn't smoke, doesn't drink, doesn't gamble
#S:=Set of Smokers
#D:=Set of drinkers
#G:=set of gamblers

#IE(S,a): Given a set S of vices and a letter a
#such that a[T] is the number of people whose set
#of vices is EXACTLY T (for any T subset of S)
#and b[T] is the number of people who have at least
#the vices of T (and possibly others)
IE:=proc(S,a,b) local Se,T,eq,Tc:
Se:=powerset(S):

#b[{Smoke}]=a[{Smoke}]+a[{Smoke,Gamble}+a[{Smoke, Drink}]+
#a[{Smoke,Drink,Gamble}]

eq:={}:

for T in Se do
Tc:=S minus T:
Tce:=powerset(Tc):

 eq:= eq union {b[T]=add(a[T union t1], t1 in Tce)}:

od:

eq:


end: