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a(n) = p^3 + p^2 where p = prime(n).
3

%I #30 May 07 2023 19:04:56

%S 12,36,150,392,1452,2366,5202,7220,12696,25230,30752,52022,70602,

%T 81356,106032,151686,208860,230702,305252,362952,394346,499280,578676,

%U 712890,922082,1040502,1103336,1236492,1306910,1455666,2064512,2265252

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

%H Ivan Panchenko, <a href="/A135178/b135178.txt">Table of n, a(n) for n = 1..1000</a>

%F Product_{n>=1} (1 - 1/a(n)) = A065465. - _Amiram Eldar_, Jan 23 2021

%e a(4)=392 because the 4th prime number is 7, 7^3=343, 7^2=49 and 343+49=392.

%p A135178:= n -> map(p -> p^(2)+p^(3), ithprime(n)):

%p seq(A135178(n), n=1..32); # _Jani Melik_, Jan 25 2010

%t Table[p=Prime[n];p^2+p^3,{n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 21 2011*)

%t #^3+#^2&/@Prime[Range[40]] (* _Harvey P. Dale_, May 07 2023 *)

%o (Magma)[ p^3 + p^2: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Dec 14 2010

%Y Cf. A000040 (p), A001248 (p^2), A030078 (p^3).

%Y Cf. A065465.

%K nonn

%O 1,1

%A _Omar E. Pol_, Nov 25 2007