This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080697 #31 Jul 13 2024 02:22:48
%S A080697 3,10,33,68,155,246,413,536,747,1090,1397,1884,2327,2674,3165,3856,
%T A080697 4709,5094,6289,7060,7707,8822,9913,11064,12725,14222,15201,16436,
%U A080697 17371,18510,21979,23648,25509,27098,30065,31572,34003,36746,38649,41240
%N A080697 a(n) = n * prime(prime(n)).
%C A080697 Previous name was: "Product of prime-index-primes and the index of their prime index".
%C A080697 Sum of reciprocals converges to about 1/2. [More accurately, 0.50056748... . - _Amiram Eldar_, Jul 13 2024]
%H A080697 Amiram Eldar, <a href="/A080697/b080697.txt">Table of n, a(n) for n = 1..10000</a>
%F A080697 a(n) = n*A006450(n). - _Omar E. Pol_, Oct 21 2013
%e A080697 a(1) = 1*prime(prime(1)) = 1*prime(2) = 1*3 = 3.
%e A080697 a(2) = 2*prime(prime(2)) = 2*prime(3) = 2*5 = 10.
%t A080697 Table[n Prime[Prime[n]], {n, 1, 40}] (* _Vincenzo Librandi_, Jun 09 2016 *)
%o A080697 (PARI) pipxindex(n) = {sr=0; pr=1; for(x=1,n, y=prime(prime(x)); pr=x*y; print1(pr" "); sr+=1.0/pr; ); print(); print(sr) }
%o A080697 (Magma) [n*NthPrime(NthPrime(n)): n in [1..40]]; // _Vincenzo Librandi_, Jun 09 2016
%Y A080697 Cf. A000040, A006450, A033286.
%K A080697 nonn,easy
%O A080697 1,1
%A A080697 _Cino Hilliard_, Mar 04 2003
%E A080697 New name from _Omar E. Pol_, Oct 21 2013