In this paper, we investigate blow-up of solutions to semilinear wave equations with scale-invariant damping and nonlinear memory term in $ \mathbb{R}^n $, which can be represented by the Riemann-Liouville fractional integral of order $ 1-\gamma $ with $ \gamma\in(0, 1) $. Our main interest is to study mixed influence from damping term and the memory kernel on blow-up conditions for the power of nonlinearity, by using test function method or generalized Kato's type lemma. We find a new competition, particularly for the small value of $ \gamma $, on the blow-up range between the effective case and the non-effective case.
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