%I #15 Jul 02 2020 04:58:58
%S 1,2,6,10,26,38,74,94,142,182,282,342,454,518,714,826,1082,1194,1434,
%T 1614,2014,2206,2590,2798,3374,3686,4362,4650,5274,5694,6526,6958,
%U 7758,8190,9246,9858,11154,11698,12786,13546,15146,15958,17366,18086,19862,20874
%N a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).
%D Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.
%H Amiram Eldar, <a href="/A333170/b333170.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (H/4) * n^3, where H = Product_{p prime, p == 1 (mod 4)} (1 - 2/p^2) = 0.8948412245... (A335963).
%e a(0) = phi(0^2 + 1) = phi(1) = 1.
%e a(1) = phi(0^2 + 1) + phi(1^2 + 1) = phi(1) + phi(2) = 1 + 1 = 2.
%t Accumulate @ Table[EulerPhi[k^2 + 1], {k, 0, 100}]
%o (PARI) a(n) = sum(k=0, n, eulerphi(k^2+1)); \\ _Michel Marcus_, Mar 10 2020
%Y Partial sums of A333169.
%Y Cf. A000010, A002522, A335963.
%K nonn
%O 0,2
%A _Amiram Eldar_, Mar 09 2020