Viscosity index improver and lube oil containing the same

A viscosity index improver, which comprises a polymer (A1) having a solubility parameter of 8.6-9.4, a crystallizing initiation temperature of −15° C. or less, and a steric hindrance factor (F) of 0-13, said factor F being defined by the following equation:

• F=4X+Y (1)
• wherein X and Y represent the total atom numbers at the 6th position and the 7th position, respectively, in the side chains, counted from the backbone;
• said polymer (A1) having a weight-average molecular weight of 5,000-2,000,000 and comprising units of at least one monomer selected from the group consisting of:
• (a) a monomer represented by the general formula:
• wherein R0 is hydrogen atom or methyl group, R is a C1-40alkyl group, n is 0 or an integer of 1-20 giving 0-10 on average, A is an alkylene group containing 2-4 carbon atoms, plural A's in case of n being at least 2 are the same or different, and the polyoxyalkylene moiety (AO)n in case of the plural A's being different comprises random-wise or block-wise distributed oxyalkylene groups,
• (b) an alkyl alkenyl ether,
• (c) an alkenyl carboxylate, and
• (d) a nitrogen-containing unsaturated monomer;
• wherein said polymer (A1) is a polymer (A12), comprising units of 27-40% by weight of an alkyl acrylate or methacrylate (a2) containing 1-4 carbon atoms in the alkyl group, 10-40% by weight of an alkyl acrylate or methacrylate (a31) containing 12-13 carbon atoms in the alkyl group, 10-40% by weight of an alkyl acrylate or methacrylate (a32) containing 14-15 carbon atoms in the alkyl group, and 5-35% by weight of an alkyl acrylate or methacrylate containing 16-40 carbon atoms in the alkyl group.