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ni11x11SupposethatSfp1p2pkgisasetofalltheprimesThensincen60ifandonlyifn1ornisaproductofcertaindistinctelementsofStakingxp1p2pk1into1iteasilyreducesto1kkXs11ksX

ni=1(1x+1):(1)SupposethatS=fp1;p2;:::;pkgisasetofalltheprimes.Thensince(n)6=0ifandonlyifn=1ornisaproductofcertain(distinct)elementsofS takingx=p1p2pk+1into(1) iteasilyreducesto(1)k+kXs=1(1)ksX

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