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%I #17 Nov 07 2022 07:39:51
%S 3,7,21,43,111,157,273,343,507,813,931,1333,1641,1807,2163,2757,3423,
%T 3661,4423,4971,5257,6163,6807,7833,9313,10101,10507,11343,11773,
%U 12657,16003,17031,18633,19183,22053,22651,24493,26407,27723,29757,31863
%N p^2-p+1 central polygonal numbers with prime indices A002061(prime(n)).
%C Prime terms belong to A074268, which is a subset of A002383, A087126, A034915, A085104.
%C 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
%F a(n) = prime(n)^2 - prime(n) + 1.
%F a(n) = A036689(n)+1. - _R. J. Mathar_, Aug 13 2019
%F Product_{n>=1} (1 - 1/a(n)) = zeta(6)/(zeta(2)*zeta(3)) (A068468). - _Amiram Eldar_, Nov 07 2022
%t Table[Prime[n]^2-Prime[n]+1,{n,1,100}]
%o (PARI) a(n) = {my(p = prime(n)); p^2 - p + 1; } \\ _Amiram Eldar_, Nov 07 2022
%Y Cf. A002061, A074268, A002383, A087126, A034915, A068468, A085104, A083558.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Aug 02 2006
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