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

1,1

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

Links

Table of n, a(n) for n=1..41.

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A097162 A128402 A018689 * A329114 A018712 A183936

Adjacent sequences: A119956 A119957 A119958 * A119960 A119961 A119962

Keyword

nonn

Author

Alexander Adamchuk, Aug 02 2006

Status

approved