A119959 - OEIS

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

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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.