<< KnotTheory`

FactorList[HOMFLYPT[Knot[9,12]][a,z]]

Cases[AllKnots[{3,10}],
K_/; Length[
Cases[
FactorList[HOMFLYPT[K][a,z]],
{f_Plus,p_}
]
]>1
]

Factor[HOMFLYPT[Knot[9,12]][a,z]]

Cases[AllKnots[{3,12}],
K_/; Length[
Cases[
FactorList[HOMFLYPT[K][a,z]],
{f_Plus,p_}
]
]>1
]

Column[
(#->Factor[HOMFLYPT[#][a,z]])&/@{Knot[9,12],Knot[11,Alternating,175],Knot[11,Alternating,176],Knot[11,Alternating,220],Knot[11,Alternating,306],Knot[12,Alternating,151],Knot[12,Alternating,165],Knot[12,Alternating,259],Knot[12,Alternating,300],Knot[12,Alternating,471],Knot[12,Alternating,505],Knot[12,Alternating,506],Knot[12,Alternating,515],Knot[12,Alternating,517],Knot[12,Alternating,535],Knot[12,NonAlternating,500]}
]