A139298 a(n) = 2^(2p - 1)/4, where p is the n-th Mersenne prime A000668(n).
8, 2048, 576460752303423488, 3618502788666131106986593281521497120414687020801267626233049500247285301248
Offset: 1
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Mathematica
a[n_] := 2^(2^(MersennePrimeExponent[n] + 1) - 5); Array[a, 4] (* Amiram Eldar, Jul 10 2025 *)