A119959 p^2-p+1 central polygonal numbers with prime indices A002061(prime(n)).

3, 7, 21, 43, 111, 157, 273, 343, 507, 813, 931, 1333, 1641, 1807, 2163, 2757, 3423, 3661, 4423, 4971, 5257, 6163, 6807, 7833, 9313, 10101, 10507, 11343, 11773, 12657, 16003, 17031, 18633, 19183, 22053, 22651, 24493, 26407, 27723, 29757, 31863

Offset: 1

Author

Alexander Adamchuk, Aug 02 2006

Keywords

• nonn

Comments

Prime terms belong to A074268, which is a subset of A002383, A087126, A034915, A085104.

In every interval of prime(n)^2 integers, a(n) is the number that are not divisible by prime(n) plus the number that are divisible by prime(n)^2. - Peter Munn, Dec 12 2020

Crossrefs

Cf. A002061, A074268, A002383, A087126, A034915, A068468, A085104, A083558.

Programs

Mathematica

Table[Prime[n]^2-Prime[n]+1,{n,1,100}]

PARI

a(n) = {my(p = prime(n)); p^2 - p + 1; } \\ Amiram Eldar, Nov 07 2022

Formula

a(n) = prime(n)^2 - prime(n) + 1.

a(n) = A036689(n)+1. - R. J. Mathar, Aug 13 2019

Product_{n>=1} (1 - 1/a(n)) = zeta(6)/(zeta(2)*zeta(3)) (A068468). - Amiram Eldar, Nov 07 2022