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a(n) = ((p+1)^(p^2) - 1)/p^3 where p = prime(n).
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%I #6 Jun 07 2021 04:42:00

%S 10,9709,227442304239437611,

%T 520133998799548061610162525309582775649689,

%U 28625475946930159815792648419743565882735766383361881336675207769030472815497554882934618500487305220787275478803827031201317381,22584369607535128530088608344394282118796031921761696815120424817179407960974433543597443656353115781613217726170809183176289639796122235605581762509509406198534210472574108288571227162377539

%N a(n) = ((p+1)^(p^2) - 1)/p^3 where p = prime(n).

%t Table[ ((Prime[n] + 1)^(Prime[n]^2) - 1)/Prime[n]^3, {n, 1, 10} ]

%Y Cf. A137641 (((n-1)^(n^2) + 1)/n^3).

%Y Cf. A133591 (((p-1)^(p^2) + 1)/p^3 where p = prime(n)).

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Jan 31 2008