%I #10 Mar 10 2020 06:31:07
%S 1,4,10,28,46,88,126,219,303,429,531,717,897,1221,1419,1761,2019,2559,
%T 2993,3539,3941,4697,5285,6257,6835,7777,8455,9787,10735,12001,12973,
%U 14569,15871,17851,19111,20953,22251,24735,26577,28863,30465,33078,35202,38736
%N a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).
%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="/A333172/b333172.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (5*G/Pi^2) * n^3, where G is Catalan's constant (A006752).
%e a(0) = sigma(0^2 + 1) = sigma(1) = 1.
%e a(1) = sigma(0^2 + 1) + sigma(1^2 + 1) = sigma(1) + sigma(2) = 1 + 3 = 4.
%t Accumulate @ Table[DivisorSigma[1, k^2 + 1], {k, 0, 100}]
%o (PARI) a(n) = sum(k=0, n, sigma(k^2+1)); \\ _Michel Marcus_, Mar 10 2020
%Y Partial sums of A193433.
%Y Cf. A000203, A002522, A006752.
%K nonn
%O 0,2
%A _Amiram Eldar_, Mar 09 2020