DESCRIPTION Title of Invention Electric Resistance Welded Steel Pipe Excellent In Deformability And Fatigue Properties After Quenching Technical Field 0001 The present invention relates to electric resistance welded steel pipe excellent in deformability and fatigue properties after quenching suitable for materials for auto parts, machine structure parts, etc. Background Art 0002 In recent years, along with the improvement in performance of automobiles and machine structures, much higher fatigue properties, more complicated part shapes, and more improved deformability of the steel material have been strongly demanded. The steel pipe which is used as material for auto parts, machine structure parts, etc. is cold worked, then machined to obtain the final part shape and adjusted in strength by subsequent quenching. Hardened auto parts and machine structure parts are required to have strength and fatigue properties. 0003 To raise the strength of steel pipe by quenching, it is necessary to raise the C content of the steel pipe material. However, high carbon steel is inferior in deformability, so the method of lowering the strength by spheroidization heat treatment has been proposed (for example, see PLT's 1 to 4). On the other hand, to improve the fatigue properties, in general it is effective to increase the hardness or strength or to impart residual stress of compression. Up until now, the method of using carburization to increase the hardness and strength of the surface layer part so as to improve the fatigue properties (see PLT 5) has been proposed. However, in recent years, from the viewpoint of lower costs and production efficiency, electric resistance welded steel pipe excellent in deformability which can be worked into complicated shapes even after omitting spheroidization heat treatment has been demanded. Further, it has been demanded to improve the fatigue properties of parts after quenching without carburization etc. 0004 Furthermore, in electric resistance welded steel pipe used for applications in which deformability is demanded, in particular, Ca is added for controlling the morphology of MnS. Further, to make the quality of the base material and the weld zone uniform, the practice has been to use electric resistance welding to make the pipe, then perform normalizing (heating to the Ac3 transformation point or more and air cooling) or other heat treatment. However, when omitting the heat treatment after pipemaking from the viewpoint of lower costs and production efficiency, according to studies of the inventors, there is the problem of deterioration of thedeformability. In steel to which Ca is added, it is demanded that the deformability not be impaired even if omitting the heat treatment after pipemaking. Citation List Patent Literature 0005 PLT 1: Japanese Patent Publication (A) No. 11-269552 PLT 2: Japanese Patent Publication (A) No. 11-269553 PLT 3: Japanese Patent Publication (A) No. 2006-9141 PLT 4: Japanese Patent Publication (A) No. 2007- 246956 PLT 5: Japanese Patent Publication (A) No. 5-117806 Summary of Invention Solution to Problem 0006 The present invention was made in consideration of this situation and provides electric resistance welded steel pipe excellent in deformability and fatigue properties after quenching which can be worked into a complicated shape without spheroidization, which can be raised in cold deformability and fatigue properties after quenching without carburization, and furthermore which is not impaired in deformability even if omitting heat treatment after pipemaking. Solution to Problem 0007 The inventors studied the effects of inclusions forming the starting points of cracks at the time of cold forging and other working and cracks in a fatigue test. As a result, they discovered that by controlling the morphology of the oxides and sulfides and other calcium(Ca)-based inclusions present at the base material and weld zone of electric resistance welded steel pipe, deformability is secured even if omitting heat treatment after pipemaking and that thereby electric resistance welded steel pipe improved in the fatigue properties after quenching can be obtained. The gist of the present invention, made in this way, is as follows: 0008 (1) An electric resistance welded steel pipe excellent in deformability and fatigue properties after quenching characterized by containing, by mass%, C: 0.15 to 0.55%, Si: 0.01 to 0.30%, Mn: 0.5 to 1.5%, Ca: 0.0010 to 0.0030%, S: 0.0005 to 0.0050%, and 0: 0.0005 to 0.0050%, restricting P: 0.020% or less, N: 0.0050% or less, and A1: 0.050% or less, having a balance of Fe and impurities, having contents of Ca, 0, and S satisfying 0.10<[Ca](1-124[0])/1.25[S]<2.50, having Ca-based inclusions present at a base material and electric resistance weld zone with an average particle size of 1,0 to 10 µm and density of 3 to 300/mm2, and having a difference AHv of a maximum hardness of the electric resistance weld zone and average hardness of a base material part of 100