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a(n) = (p+1)*(p+2)/2 where p is the n-th prime.
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%I #14 Sep 08 2022 08:46:16

%S 6,10,21,36,78,105,171,210,300,465,528,741,903,990,1176,1485,1830,

%T 1953,2346,2628,2775,3240,3570,4095,4851,5253,5460,5886,6105,6555,

%U 8256,8778,9591,9870,11325,11628,12561,13530,14196,15225,16290,16653,18528,18915,19701

%N a(n) = (p+1)*(p+2)/2 where p is the n-th prime.

%C Subsequence of A253145.

%H Vincenzo Librandi, <a href="/A271511/b271511.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[(Prime[n]^2 + 3 Prime[n] + 2) / 2, {n, 50}]

%o (Magma) [(p+1)*(p+2) / 2: p in PrimesUpTo(200)];

%o (PARI) lista(nn) = forprime(p=2, nn, print1((p+1)*(p+2)/2, ", ")); \\ _Altug Alkan_, Apr 09 2016

%Y Cf. A253145.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Apr 09 2016