This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333170 #15 Jul 02 2020 04:58:58 %S A333170 1,2,6,10,26,38,74,94,142,182,282,342,454,518,714,826,1082,1194,1434, %T A333170 1614,2014,2206,2590,2798,3374,3686,4362,4650,5274,5694,6526,6958, %U A333170 7758,8190,9246,9858,11154,11698,12786,13546,15146,15958,17366,18086,19862,20874 %N A333170 a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010). %D A333170 Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166. %H A333170 Amiram Eldar, <a href="/A333170/b333170.txt">Table of n, a(n) for n = 0..10000</a> %F A333170 a(n) ~ (H/4) * n^3, where H = Product_{p prime, p == 1 (mod 4)} (1 - 2/p^2) = 0.8948412245... (A335963). %e A333170 a(0) = phi(0^2 + 1) = phi(1) = 1. %e A333170 a(1) = phi(0^2 + 1) + phi(1^2 + 1) = phi(1) + phi(2) = 1 + 1 = 2. %t A333170 Accumulate @ Table[EulerPhi[k^2 + 1], {k, 0, 100}] %o A333170 (PARI) a(n) = sum(k=0, n, eulerphi(k^2+1)); \\ _Michel Marcus_, Mar 10 2020 %Y A333170 Partial sums of A333169. %Y A333170 Cf. A000010, A002522, A335963. %K A333170 nonn %O A333170 0,2 %A A333170 _Amiram Eldar_, Mar 09 2020