A267144 - OEIS

%I #14 Feb 16 2025 08:33:29

%S 8,21,65,133,341,481,833,1045,1541,2465,2821,4033,4961,5461,6533,8321,

%T 10325,11041,13333,14981,15841,18565,20501,23585,28033,30401,31621,

%U 34133,35425,38081,48133,51221,56033,57685,66305,68101,73633,79381,83333,89441,95765

%N Octagonal numbers with prime indices.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeNumber.html">Prime Number</a>

%F a(n) = prime(n)*(3*prime(n) - 2) = A000040(n)*(3*A000040(n) - 2).

%F a(n) = A000567(A000040(n)).

%F a(n) = sigma_0(24^(prime(n) - 1)) = A000005(A009968(A000040(n) - 1)).

%t Table[Prime[n] (3 Prime[n] - 2), {n, 1, 45}]

%o (PARI) lista(nn) = forprime(p=2, nn, print1(p*(3*p-2), ", ")); \\ _Altug Alkan_, Jan 11 2016

%o (Magma) [NthPrime(n)*(3*NthPrime(n)-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 12 2016

%o (Python)

%o from sympy import prime

%o def a(n): p = prime(n); return p*(3*p-2)

%o print([a(n) for n in range(1, 42)]) # _Michael S. Branicky_, Aug 21 2021

%Y Cf. A000040, A000567, A001248, A034953, A116995, A117961.

%K nonn,easy

%O 1,1

%A _Ilya Gutkovskiy_, Jan 11 2016