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We consider when certain Banach sequence algebras A on the set N are approximately amenable. Some general results are obtained, and we resolve the special cases where A = ℓ p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ℓ p (ω).doi:10.4064/sm177-1-6 fatcat:5tnbfqhsl5hobjd5z2omsew4na