# OK to post homework
# Vikrant, Apr 10 2022, Assignment 21

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# 0. Code that has been given.
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read("C21.txt"):

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# 1. Fix JTseq.
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JTseq:=
    proc(N)
        local n,La,Lb,L,b,l:
        La:=aSeq(N):
        Lb:=bSeq(3*N):
        L:=[]:
        for n from 1 to N do
            b:= IsSquareFree(n) and La[n]=0 and (n mod 2=1 or Lb[n/2]=0):
            for l in L do
                b:= evalb(b or type(sqrt(n/l),integer)):
            od:
            if b then
                L:=[op(L),n]:
            fi:
        od:
        L:   
    end:

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# 2. Square-freeness.
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IsSquareFree:=
    proc(N)
        evalb(add(ifactors(N)[2])[2]=nops(ifactors(N)[2])):
    end:

IsCon:=
    proc(n):
        if n mod 2=1 and 2*nops(Tn(n,2,1,32))=nops(Tn(n,2,1,8)) then
            RETURN(IsSquareFree(n)):
        elif n mod 2=0 and  2*nops(Tn(n,8,2,64))=nops(Tn(n,8,2,16)) then
            RETURN(IsSquareFree(n)):
        fi:
        false:
    end:

JTseqW:=
    proc(N)
        local n,L,l,b:
        L:=[]:
        for n from 1 to N do
            b:= IsCon(n):
            for l in L do
                b:= evalb(b or type(sqrt(n/l),integer)):
            od:
            if b then
                L:=[op(L),n]:
            fi:
        od:
        L:
    end:

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# 3. <Skipped>
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# 4. <Skipped>
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