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Let $\mathbb{Y}$ be either an Orlicz sequence space or a Marcinkiewiczsequence space. We take advantage of the recent advances in the theory offactorization of the identity carried on in [R. Lechner, Subsymmetric weak*Schauder bases and factorization of the identity, arXiv:1804.01372 [math.FA]]to provide conditions on $\mathbb{Y}$ that ensure that, for any $1\lep\le\infty$, the infinite direct sum of $\mathbb{Y}$ in the sense of $\ell_p$is a primary Banach space, enlarging this way the list of Banach spaces thatare known to be primary.

Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces