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A135178 a(n) = p^3 + p^2 where p = prime(n).

%I A135178 #32 Mar 31 2025 14:37:33
%S A135178 12,36,150,392,1452,2366,5202,7220,12696,25230,30752,52022,70602,
%T A135178 81356,106032,151686,208860,230702,305252,362952,394346,499280,578676,
%U A135178 712890,922082,1040502,1103336,1236492,1306910,1455666,2064512,2265252
%N A135178 a(n) = p^3 + p^2 where p = prime(n).
%H A135178 Ivan Panchenko, <a href="/A135178/b135178.txt">Table of n, a(n) for n = 1..1000</a>
%F A135178 Product_{n>=1} (1 - 1/a(n)) = A065465. - _Amiram Eldar_, Jan 23 2021
%F A135178 Sum 1/a(n) = A382562.
%e A135178 a(4)=392 because the 4th prime number is 7, 7^3=343, 7^2=49 and 343+49=392.
%p A135178 A135178:= n -> map(p -> p^(2)+p^(3), ithprime(n)):
%p A135178 seq(A135178(n), n=1..32); #  _Jani Melik_, Jan 25 2010
%t A135178 Table[p=Prime[n];p^2+p^3,{n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 21 2011*)
%t A135178 #^3+#^2&/@Prime[Range[40]] (* _Harvey P. Dale_, May 07 2023 *)
%o A135178 (Magma)[ p^3 + p^2: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Dec 14 2010
%Y A135178 Cf. A000040 (p), A001248 (p^2), A030078 (p^3).
%Y A135178 Cf. A065465.
%K A135178 nonn
%O A135178 1,1
%A A135178 _Omar E. Pol_, Nov 25 2007