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a(n) = A051903(A072055(n)). - Amiram Eldar, Sep 09 2024
a[n_] := Max[FactorInteger[2*Prime[n] + 1][[;; , 2]]]; Array[a, 100] (* Amiram Eldar, Sep 09 2024 *)
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(PARI) a(n) = vecmax(factor(2*prime(n)+1)[, 2]); \\ Michel Marcus, Apr 20 2021
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Greatest exponent in prime-power factorization of 2*pprime(n)+1.
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Clark Kimberling (ck6(AT)evansville.edu)