%I #18 Nov 28 2022 01:57:53
%S 0,1,0,1,2,1,2,3,3,3,4,4,5,6,6,6,8,7,9,9,9,10,11,11,12,12,13,14,13,14,
%T 16,17,17,18,18,19,19,21,21,21,23,22,24,24,24,25,27,28,29,28,29,30,30,
%U 32,32,33,33,34,34,35,36,36,39,39,39,39,42,42,44,43,44
%N Number of representations of square of prime(n) as a^2 + b^2 + c^2 with 0 < a <= b <= c.
%C Almost monotonically increasing sequence, only rarely a(n) <= a(n-1), contrary to case of n instead of prime(n) (A181786).
%H Samuel Harkness, <a href="/A208882/b208882.txt">Table of n, a(n) for n = 1..1229</a>
%e a(2)=1 because prime(2)=3 and 3^2 = 1^2 + 2^2 + 2^2,
%e a(4)=1 because prime(4)=7 and 7^2 = 2^2 + 3^2 + 6^2,
%e a(5)=2 because prime(5)=11 and 11^2 = 2^2 + 6^2 + 9^2 = 6^2 + 6^2 + 7^2.
%t Table[Length[FindInstance[{Prime[n]^2==a^2+b^2+c^2,0<a<=b<=c},{a,b,c},Integers,100]],{n,80}] (* _Harvey P. Dale_, Mar 06 2020 *)
%Y Cf. A002144, A181786.
%K nonn
%O 1,5
%A _Zak Seidov_, Mar 02 2012