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a(n) = n * prime(prime(n)).
4

%I #31 Jul 13 2024 02:22:48

%S 3,10,33,68,155,246,413,536,747,1090,1397,1884,2327,2674,3165,3856,

%T 4709,5094,6289,7060,7707,8822,9913,11064,12725,14222,15201,16436,

%U 17371,18510,21979,23648,25509,27098,30065,31572,34003,36746,38649,41240

%N a(n) = n * prime(prime(n)).

%C Previous name was: "Product of prime-index-primes and the index of their prime index".

%C Sum of reciprocals converges to about 1/2. [More accurately, 0.50056748... . - _Amiram Eldar_, Jul 13 2024]

%H Amiram Eldar, <a href="/A080697/b080697.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n*A006450(n). - _Omar E. Pol_, Oct 21 2013

%e a(1) = 1*prime(prime(1)) = 1*prime(2) = 1*3 = 3.

%e a(2) = 2*prime(prime(2)) = 2*prime(3) = 2*5 = 10.

%t Table[n Prime[Prime[n]], {n, 1, 40}] (* _Vincenzo Librandi_, Jun 09 2016 *)

%o (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 (Magma) [n*NthPrime(NthPrime(n)): n in [1..40]]; // _Vincenzo Librandi_, Jun 09 2016

%Y Cf. A000040, A006450, A033286.

%K nonn,easy

%O 1,1

%A _Cino Hilliard_, Mar 04 2003

%E New name from _Omar E. Pol_, Oct 21 2013