A267144 Octagonal numbers with prime indices.

8, 21, 65, 133, 341, 481, 833, 1045, 1541, 2465, 2821, 4033, 4961, 5461, 6533, 8321, 10325, 11041, 13333, 14981, 15841, 18565, 20501, 23585, 28033, 30401, 31621, 34133, 35425, 38081, 48133, 51221, 56033, 57685, 66305, 68101, 73633, 79381, 83333, 89441, 95765

Offset: 1

Author

Ilya Gutkovskiy, Jan 11 2016

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Octagonal Number
• Eric Weisstein's World of Mathematics, Prime Number

Crossrefs

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

Programs

Magma

[NthPrime(n)*(3*NthPrime(n)-2): n in [1..50]]; // Vincenzo Librandi, Jan 12 2016

Mathematica

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

PARI

lista(nn) = forprime(p=2, nn, print1(p*(3*p-2), ", ")); \\ Altug Alkan, Jan 11 2016

Python

from sympy import prime
def a(n): p = prime(n); return p*(3*p-2)
print([a(n) for n in range(1, 42)]) # Michael S. Branicky, Aug 21 2021

Formula

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

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

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