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For all n, a(n) <> A335882(n). Proof: We need to consider only the odd terms, because for n > 1, A332215(2^k * n) = 2^k * A332215(n). The odd terms of A335882 are either primes or semiprimes whose both factors are Mersenne primes, terms of A144482.

(A) If A335882(n) is a prime, then a(n) = A332215(A335882(n)) is a term of A000225 (of the form 2^k - 1, a binary repunit), while primes in A335882 are certainly not of that form, as all Mersenne primes (A000668) are on a different row in array A335430 (on row 1, A335431).

(B) For any semiprime k in A335882, there is only one non-leading zero in the binary representation of A332215(k). On the other hand, a product of two Mersenne primes always contains more than one non-leading zero in its base-2 representation: for three times a Mersenne prime, there are two such zeros, as explained in A279389, and products of two Mersenne primes > 3 are always of the form 8k+1, with at least two zeros immediately left of the least significant 1-bit.