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%I #14 Sep 08 2022 08:45:19
%S 2,14,24,70,114,140,234,310,444,660,784,850,990,1064,1564,1850,2054,
%T 2494,2730,3104,3234,4370,4524,4840,5504,6030,6394,6580,7154,8164,
%U 8374,9464,10150,10384,11594,12610,13134,13400,13940,14770,15624,16800,17404
%N a(n) = (p^2 - 1) / 12, where p is the n-th prime of the form 4*k+1.
%D G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 2, Problem 20.
%H Michael De Vlieger, <a href="/A109255/b109255.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A002144(n)^2 - 1) / 12.
%F a(n) = Sum_{k=1..(p-1)/4} floor(sqrt(k*p)), where p = primes of the form 4*n+1.
%t Map[(#^2 - 1)/12 &, Select[4 Range[120] + 1, PrimeQ]] (* _Michael De Vlieger_, Dec 27 2019 *)
%o (Magma) [(p^2 - 1) / 12: p in PrimesUpTo(500)| p mod 4 eq 1]; // _Marius A. Burtea_, Dec 29 2019
%Y Cf. A002144.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Aug 20 2005