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A333172 a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).

%I A333172 #10 Mar 10 2020 06:31:07
%S A333172 1,4,10,28,46,88,126,219,303,429,531,717,897,1221,1419,1761,2019,2559,
%T A333172 2993,3539,3941,4697,5285,6257,6835,7777,8455,9787,10735,12001,12973,
%U A333172 14569,15871,17851,19111,20953,22251,24735,26577,28863,30465,33078,35202,38736
%N A333172 a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).
%D A333172 Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.
%H A333172 Amiram Eldar, <a href="/A333172/b333172.txt">Table of n, a(n) for n = 0..10000</a>
%F A333172 a(n) ~ (5*G/Pi^2) * n^3, where G is Catalan's constant (A006752).
%e A333172 a(0) = sigma(0^2 + 1) = sigma(1) = 1.
%e A333172 a(1) = sigma(0^2 + 1) + sigma(1^2 + 1) = sigma(1) + sigma(2) = 1 + 3 = 4.
%t A333172 Accumulate @ Table[DivisorSigma[1, k^2 + 1], {k, 0, 100}]
%o A333172 (PARI) a(n) = sum(k=0, n, sigma(k^2+1)); \\ _Michel Marcus_, Mar 10 2020
%Y A333172 Partial sums of A193433.
%Y A333172 Cf. A000203, A002522, A006752.
%K A333172 nonn
%O A333172 0,2
%A A333172 _Amiram Eldar_, Mar 09 2020