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We construct a filtered mapping cone formula that computes the knot Floercomplex of the $(n,1)$--cable of the knot meridian in any rational surgery,generalizing Truong's result about the $(n,1)$--cable of the knot meridian inlarge surgery and Hedden-Levine's filtered mapping cone formula. As anapplication, we show that there exist knots in integer homology spheres witharbitrary $\varphi_{i,j}$ values for any $i>j\geq 0$, where $\varphi_{i,j}$ arethe concordance homomorphisms defined by Dai-Hom-Stoffregen-Truong.

A filtered mapping cone formula for cables of the knot meridian