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In JT-60U, simultaneous excitation of n = 1 helical cores (HCs) and m/n = 2/1 Tearing Modes (TMs) was observed [T. Bando et al., Plasma Phys. Control. Fusion 61 115014 (2019)]. In this paper, we have investigated the excitation mechanism of n = 1 HCs with m/n = 2/1 TMs based on the experimental observations and a simple quasi-linear MHD model. In the previous study, it was reported that a "coupling" on the phase of the MHD mode is observed between n = 1 HCs and m/n = 2/1 TMs. In this study, it is found that the coupling is observed with the mode frequency from several Hz to 6 kHz. This indicates that the resistive wall and the plasma control system do not induce the coupling because the both time scales are different from the mode frequency. In addition, n = 1 HCs appear to be the non-resonant mode from the two observations: n = 1 HCs do not rotate with the plasma around the q = 1 surface in the core and the coupling is also observed even when qmin > 1. It is also observed that the electron fluctuation due to an n = 1 HC in the core region disappears with the stabilization of an m/n = 2/1 neoclassical tearing mode by electron cyclotron current drive, implying that n = 1 HCs are driven by m/n = 2/1 TMs. This perspective, n = 1 HCs are driven by m/n = 2/1 TMs, is supported by the observation that the saturated amplitude of the m/n = 1/1 component of the radial displacement in the core is smaller than that of the m/n = 2/1 component. Finally, we revisit a quasi-linear MHD model where the m/n = 1/1 HC is induced directly by the sideband of the current for the m/n = 2/1 TM, which allows to excite the non-resonant m/n = 1/1 mode. The model also describes the characteristic of the coupling, fm/n=1/1(HC) = 2fm/n=2/1(TM).